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A362790
a(n) = Sum_{k=0..n} FallingFactorial(n - k, k) * Stirling2(n - k, k), row sums of A362789.
2
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, May 04 2023
STATUS
approved