OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..227
FORMULA
a(n) = Sum_{k=0..n} k^(3*n-2*k).
a(n) ~ sqrt(Pi) * (3/2)^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) * (n/LambertW(3*exp(1)*n/2))^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) / sqrt(1 + LambertW(3*exp(1)*n/2)). - Vaclav Kotesovec, Dec 04 2021
MATHEMATICA
a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 04 2021 *)
PROG
(PARI) a(n, t=3) = sum(k=0, n, k^(t*(n-k)+k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^3*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 03 2021
STATUS
approved