A353018 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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))