A353018 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-3*k).

1, 1, 4, 28, 257, 3129, 46684, 823800, 16780345, 387467173, 10000823800, 285328450956, 8916487915429, 302885107416053, 11112292154008972, 437902806868774804, 18447046958816967669, 827251374178490773149, 39346845978103406350228

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

a[n_] := Sum[If[3*k == n, 1, (n - 3*k)^(n - 3*k)], {k, 0, Floor[n/3]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)

Prog

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

Crossrefs

Cf. A062970, A353009.

Cf. A001840, A353014, A353015.

Sequence in context: A002895 A294189 A350145 * A141004 A217806 A356197

Adjacent sequences: A353015 A353016 A353017 * A353019 A353020 A353021

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 16 2022

Status

approved