A357194 a(n) = n! * Sum_{k=0..floor(n/3)} k^(3*n)/k!.

1, 0, 0, 6, 24, 120, 94372560, 5284828080, 338228714880, 461220488356944960, 124524904888012809600, 36983489578531184304000, 94262861823240343196388902400, 78420937396722501660156363686400, 70262981254649802508019882162611200

Offset: 0

Author

Seiichi Manyama, Sep 17 2022

Keywords

• nonn

Crossrefs

Cf. A256016, A357193.

Cf. A352984, A357192.

Programs

PARI

a(n) = n!*sum(k=0, n\3, k^(3*n)/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*x)^(3*k)/(k!*(1-k^3*x)))))

Formula

E.g.f.: Sum_{k>=0} (k^3 * x)^(3 * k) / (k! * (1 - k^3 * x)).