A356672 a(n) = n! * Sum_{k=0..n} k^(2*(n-k))/k!.

1, 1, 3, 19, 253, 5661, 188191, 8983423, 594848409, 52174034713, 5852229698971, 822684190381131, 142739480367287893, 30074750245383836149, 7575373641076070706423, 2252600759590927171373431, 783103569459739402827046321, 315587346190678252431713684913

Offset: 0

Author

Seiichi Manyama, Aug 22 2022

Keywords

• nonn

Crossrefs

Cf. A354436, A356673.

Cf. A234568, A356628.

Programs

PARI

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

PARI

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

Formula

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