A367272 a(n) = Sum_{k=0..n} binomial(n, k)^2 * k^(n - k).

1, 1, 5, 28, 209, 1826, 18217, 203106, 2487361, 33077566, 473318201, 7234847126, 117435618577, 2014339775800, 36360190887217, 688237505878726, 13618646813974785, 280960214041690038, 6028928694559721305, 134277542969681115870, 3098232871805383942801

Offset: 0

Author

Peter Luschny, Nov 11 2023

Keywords

• nonn

Crossrefs

Cf. A059297.

Programs

Maple

a := n -> add(binomial(n, k)^2*k^(n - k), k = 0 .. n):
seq(a(n), n = 0..22);

Mathematica

Join[{1}, Table[Sum[Binomial[n,k]^2 * k^(n-k), {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 12 2023 *)

Formula

a(n) = Sum_{k=0..n} binomial(n, k) * A059297(n, k).

log(a(n)) ~ n*(log(n) - log(log(n)) - 1 + (3*log(log(n)) + 2)/log(n) - 1/log(n)^2). - Vaclav Kotesovec, Nov 12 2023