A256549 Triangle read by rows, T(n,k) = {n,k}*h(k), where {n,k} are the Stirling set numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.

1, 0, 1, 0, 1, 3, 0, 1, 9, 13, 0, 1, 21, 78, 73, 0, 1, 45, 325, 730, 501, 0, 1, 93, 1170, 4745, 7515, 4051, 0, 1, 189, 3913, 25550, 70140, 85071, 37633, 0, 1, 381, 12558, 124173, 526050, 1077566, 1053724, 394353, 0, 1, 765, 39325, 567210, 3482451, 10718946, 17386446, 14196708, 4596553

Offset: 0

Author

Peter Luschny, Apr 12 2015

Keywords

• nonn
• tabl
• easy

Examples

			Triangle starts:
[1]
[0, 1]
[0, 1,  3]
[0, 1,  9,   13]
[0, 1, 21,   78,   73]
[0, 1, 45,  325,  730,  501]
[0, 1, 93, 1170, 4745, 7515, 4051]
		

Crossrefs

Cf. A000110, A000262, A048993, A068156, A075729.

Programs

Sage

A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
A256549 = lambda n,k: A000262(k)*stirling_number2(n,k)
for n in range(7): [A256549(n,k) for k in (0..n)]

Formula

Row sums are A075729.

Alternating row sums are the signed Bell numbers (-1)^n*A000110(n).

T(n,k) = A048993(n,k)*A000262(k).

T(n,n) = A000262(n).

T(n+2,2) = A068156(n).