Lah numbers: Difference between revisions

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=={{header|Julia}}==

<lang julia>using Combinatorics

function lah(n, k, signed=false)

if n == 0 | k == 0

return 0

elseif n == k

return 1

elseif k == 1

return factorial(n)

else

unsignedvalue = binomial(n, k) * binomial(n - 1, k - 1) * factorial(n - k)

if signed && isodd(n)

return -1 * unsignedvalue

else

return unsignedvalue

end

end

end

function printlahtable(kmax)

println(" ", mapreduce(i -> lpad(i, 12), *, 0:kmax))

sstring(n, k) = begin i = (n >= k) ? lah(n, k) : 0; lpad(k > n && i == 0 ? "" : i, 12) end

for n in 0:kmax

println(rpad(n, 2) * mapreduce(k -> sstring(n, k), *, 0:kmax))

end

end

printlahtable(12)

println("\nThe maxiumum of lah(100, _) is: ", maximum(k -> lah(BigInt(100), BigInt(k)), 1:100))

</lang>{{out}}

<pre>

0 1 2 3 4 5 6 7 8 9 10 11 12

0 0

1 0 1

2 0 2 1

3 0 6 6 1

4 0 24 36 12 1

5 0 120 240 120 20 1

6 0 720 1800 1200 300 30 1

7 0 5040 15120 12600 4200 630 42 1

8 0 40320 141120 141120 58800 11760 1176 56 1

9 0 362880 1451520 1693440 846720 211680 28224 2016 72 1

10 0 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1

11 0 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1

12 0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1

The maxiumum of lah(100, _) is: 44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000