A357174 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^n/(n - 3*k)!.

1, 1, 4, 27, 280, 5045, 134136, 4269223, 153188176, 6657007113, 371930499280, 25072409219891, 1872319689314856, 154583203638018493, 14784597239881491400, 1641532369038107170815, 201617558936011146124576, 26755058016106471234608017

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Mathematica

a[n_] := n! * Sum[(n - 3*k)^n/(n - 3*k)!, {k, 0, Floor[n/3]} ]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Sep 16 2022 *)

Prog

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

Crossrefs

Cf. A256016, A356834.

Cf. A353015, A357147.

Sequence in context: A259485 A362699 A193467 * A377811 A179494 A295255

Adjacent sequences: A357171 A357172 A357173 * A357175 A357176 A357177

Keyword

nonn

Author

Seiichi Manyama, Sep 16 2022

Status

approved