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

Author

Peter Luschny, May 04 2023

Keywords

• nonn

Crossrefs

Cf. A362789.

Programs

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);

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)])