A256548 Triangle read by rows, T(n,k) = |n,k|*h(k), where |n,k| are the Stirling cycle numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.

1, 0, 1, 0, 1, 3, 0, 2, 9, 13, 0, 6, 33, 78, 73, 0, 24, 150, 455, 730, 501, 0, 120, 822, 2925, 6205, 7515, 4051, 0, 720, 5292, 21112, 53655, 87675, 85071, 37633, 0, 5040, 39204, 170716, 494137, 981960, 1304422, 1053724, 394353

Offset

0,6

Links

Table of n, a(n) for n=0..44.

Formula

T(n,k) = A132393(n,k)*A000262(k).

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

T(n+1,1) = n!.

Row sums are A088815.

Alternating row sums are (-1)^n*A088819(n).

Example

Triangle starts:
[1]
[0,   1]
[0,   1,   3]
[0,   2,   9,   13]
[0,   6,  33,   78,   73]
[0,  24, 150,  455,  730,  501]
[0, 120, 822, 2925, 6205, 7515, 4051]

Prog

(Sage)
A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
A256548 = lambda n, k: A000262(k)*stirling_number1(n, k)
for n in range(7): [A256548(n, k) for k in (0..n)]

Crossrefs

Cf. A000262, A088815, A088819, A132393, A256549.

Sequence in context: A193084 A126598 A326602 * A239098 A319501 A302224

Adjacent sequences: A256545 A256546 A256547 * A256549 A256550 A256551

Keyword

nonn,tabl,easy

Author

Peter Luschny, Apr 12 2015

Status

approved