Stirling numbers of the first kind: Difference between revisions

=={{header|FreeBASIC}}==

<lang freebasic>dim as integer S1(0 to 12, 0 to 12) 'initially set with zeroes

dim as ubyte n, k

dim as string outstr

function padto( i as ubyte, j as integer ) as string

return wspace(i-len(str(j)))+str(j)

end function

S1(0, 0) = 1

for n = 0 to 12 'calculate table

for k = 1 to n

S1(n, k) = S1(n-1, k-1) - (n-1) * S1(n-1, k)

next k

next n

print "Signed Stirling numbers of the first kind"

print

outstr = " k"

for k=0 to 12

outstr += padto(12, k)

next k

print outstr

print " n"

for n = 0 to 12

outstr = padto(2, n)+" "

for k = 0 to 12

outstr += padto(12, S1(n, k))

next k

print outstr

next n</lang>

<pre>Signed Stirling numbers of the first kind

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

n

0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 0 0 0 0 0 0 0 0 0 0 0

2 0 -1 1 0 0 0 0 0 0 0 0 0 0

3 0 2 -3 1 0 0 0 0 0 0 0 0 0

4 0 -6 11 -6 1 0 0 0 0 0 0 0 0

5 0 24 -50 35 -10 1 0 0 0 0 0 0 0

6 0 -120 274 -225 85 -15 1 0 0 0 0 0 0

7 0 720 -1764 1624 -735 175 -21 1 0 0 0 0 0

8 0 -5040 13068 -13132 6769 -1960 322 -28 1 0 0 0 0

9 0 40320 -109584 118124 -67284 22449 -4536 546 -36 1 0 0 0

10 0 -362880 1026576 -1172700 723680 -269325 63273 -9450 870 -45 1 0 0

11 0 3628800 -10628640 12753576 -8409500 3416930 -902055 157773 -18150 1320 -55 1 0

12 0 -39916800 120543840 -150917976 105258076 -45995730 13339535 -2637558 357423 -32670 1925 -66 1</pre>