A362790 - OEIS

%I #5 May 04 2023 08:56:42

%S 1,0,1,2,5,22,95,450,2461,14654,93851,647746,4781801,37488462,

%T 310842127,2716308194,24929090357,239556785086,2404139609987,

%U 25139451248418,273330944247265,3084182865509966,36055337388402935,436016786153035522,5446585683469420205

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

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

%p seq(a(n), n = 0..24);

%o (SageMath)

%o def A362790(n):

%o     return sum(falling_factorial(n - k, k) * stirling_number2(n - k, k) for k in range(n//2 + 1))

%o print([A362790(n) for n in range(12)])

%Y Cf. A362789.

%K nonn

%O 0,4

%A _Peter Luschny_, May 04 2023