A353014 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(n-2*k).

1, 1, 4, 27, 257, 3133, 46737, 824568, 16792857, 387700668, 10005768898, 285445966496, 8919588913002, 302975146962245, 11115146328067250, 438000914977377939, 18450682450377791691, 827395864513198608177, 39352977767853205024131

Offset: 0

Author

Seiichi Manyama, Apr 16 2022

Keywords

• nonn
• easy

Crossrefs

Cf. A031971, A353013.

Cf. A352946, A353015.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[(n - 3*k)^(n - 2*k), {k, 0, Floor[n/3]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)

PARI

a(n) = sum(k=0, n\3, (n-3*k)^(n-2*k));

PARI

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

Formula

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