A362790 a(n) = Sum_{k=0..n} FallingFactorial(n - k, k) * Stirling2(n - k, k), row sums of A362789.

1, 0, 1, 2, 5, 22, 95, 450, 2461, 14654, 93851, 647746, 4781801, 37488462, 310842127, 2716308194, 24929090357, 239556785086, 2404139609987, 25139451248418, 273330944247265, 3084182865509966, 36055337388402935, 436016786153035522, 5446585683469420205

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Maple

a := n -> add((-1)^k*pochhammer(k - n, k)*Stirling2(n - k, k), k = 0..iquo(n, 2)):
seq(a(n), n = 0..24);

Prog

(SageMath)
def A362790(n):
    return sum(falling_factorial(n - k, k) * stirling_number2(n - k, k) for k in range(n//2 + 1))
print([A362790(n) for n in range(12)])

Crossrefs

Cf. A362789.

Sequence in context: A346628 A371609 A030222 * A369830 A056840 A321608

Adjacent sequences: A362787 A362788 A362789 * A362791 A362792 A362793

Keyword

nonn

Author

Peter Luschny, May 04 2023

Status

approved