A357191 a(n) = n! * Sum_{k=0..floor(n/2)} k^n/k!.

1, 0, 2, 6, 216, 2040, 111240, 2164680, 159391680, 5247305280, 491431600800, 24437592194400, 2800955712804480, 195393943295591040, 26699221909806526080, 2479967110139382864000, 396503602252401676032000, 47167550656581451928832000

Offset: 0

Author

Seiichi Manyama, Sep 17 2022

Keywords

• nonn

Crossrefs

Cf. A256016, A357192.

Cf. A352981, A357193.

Programs

PARI

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

PARI

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

Formula

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