A357147 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^(3*k)/(n - 3*k)!.

1, 1, 1, 1, 25, 481, 3241, 18481, 1332241, 44198785, 623190961, 15416707681, 1602405014761, 68167258954081, 1598025440555545, 134130467333575441, 14793638741719612321, 730659540435131811841, 34674365632872552887521, 5776415685538277157146305

Offset: 0

Author

Seiichi Manyama, Sep 15 2022

Keywords

• nonn

Crossrefs

Cf. A354436, A357146.

Cf. A353017, A356629.

Programs

PARI

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

PARI

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

Formula

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