Lah numbers: Difference between revisions
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The maximum l(100,k): 4451900544899314481...0000000000000000000 (164 digits) |
The maximum l(100,k): 4451900544899314481...0000000000000000000 (164 digits) |
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</pre> |
</pre> |
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=={{header|Python}}== |
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<lang python>def factorial(n): |
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if n == 0: |
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return 1 |
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res = 1 |
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while n > 0: |
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res *= n |
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n -= 1 |
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return res |
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def lah(n,k): |
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if k == 1: |
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return factorial(n) |
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if k == n: |
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return 1 |
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if k > n: |
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return 0 |
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if k < 1 or n < 1: |
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return 0 |
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return (factorial(n) * factorial(n - 1)) / (factorial(k) * factorial(k - 1)) / factorial(n - k) |
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def main(): |
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print "Unsigned Lah numbers: L(n, k):" |
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print "n/k ", |
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for i in xrange(13): |
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print "%11d" % i, |
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print |
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for row in xrange(13): |
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print "%-4d" % row, |
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for i in xrange(row + 1): |
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l = lah(row, i) |
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print "%11d" % l, |
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print |
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print "\nMaximum value from the L(100, *) row:" |
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maxVal = max([lah(100, a) for a in xrange(100)]) |
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print maxVal |
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main()</lang> |
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{{out}} |
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<pre>Unsigned Lah numbers: L(n, k): |
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n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 |
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0 1 |
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1 0 1 |
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2 0 2 1 |
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3 0 6 6 1 |
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4 0 24 36 12 1 |
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5 0 120 240 120 20 1 |
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6 0 720 1800 1200 300 30 1 |
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7 0 5040 15120 12600 4200 630 42 1 |
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8 0 40320 141120 141120 58800 11760 1176 56 1 |
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9 0 362880 1451520 1693440 846720 211680 28224 2016 72 1 |
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10 0 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1 |
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11 0 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1 |
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12 0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1 |
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Maximum value from the L(100, *) row: |
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44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre> |
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=={{header|REXX}}== |
=={{header|REXX}}== |