A356834 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^n/(n - 2*k)!.

1, 1, 4, 33, 448, 8105, 192576, 5946913, 226097152, 10389920913, 571788928000, 36818407010561, 2741300619657216, 234014330510734969, 22620660476040331264, 2457467449742570271105, 298061856229112792743936, 40058727579693211737837857

Offset: 0

Author

Seiichi Manyama, Sep 16 2022

Keywords

• nonn

Crossrefs

Cf. A256016, A357174.

Cf. A352082, A357146.

Programs

Maple

f:= proc(n) local k;  n! * add((n-2*k)^n/(n-2*k)!,k=0..floor(n/2)) end proc:
map(f, [$0..20]); # Robert Israel, Sep 16 2022

Mathematica

a[n_] := n! * Sum[(n - 2*k)^n/(n - 2*k)!, {k, 0, Floor[n/2]} ]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Sep 16 2022 *)

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k)^n/(n-2*k)!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^k/(k!*(1-(k*x)^2)))))

Formula

E.g.f.: Sum_{k>=0} (k * x)^k / (k! * (1 - (k * x)^2)).