A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k).

0, 1, 6, 57, 712, 10905, 197136, 4102777, 96552576, 2534382513, 73397843200, 2324613341721, 79923267523584, 2964436169152393, 117986961509824512, 5015721009078977625, 226816401312675168256, 10871698383944129824353, 550571805478900954497024

Offset: 0

Author

Peter Luschny, Jan 13 2024

Keywords

• nonn

Crossrefs

Cf. Row sums of A369019.

Programs

Maple

A369071 := n -> local k; add(binomial(n, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k), k=0..n): seq(A369071(n), n = 0..18);

Mathematica

A369071[n_] := Sum[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k), {k, n}]; Array[A369071, 20, 0] (* Paolo Xausa, Jan 28 2024 *)

SageMath

def A369071(n):
    return sum(binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k)
           for k in range(n + 1))
print([A369071(n) for n in range(11)])