A349901 - OEIS

%I #16 Dec 06 2021 03:09:22

%S 1,1,65,20196,17312754,31605701625,105443761093411,580964060390826448,

%T 4918745981990731659972,60634331963604550954204425,

%U 1043651859661187698792930519525,24256699178432730349549665042311076,740737411098120942914045235001015624310

%N a(n) = Sum_{k=0..n} k^(3*n).

%H Seiichi Manyama, <a href="/A349901/b349901.txt">Table of n, a(n) for n = 0..152</a>

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

%F a(n) ~ exp(3)/(exp(3)-1) * n^(3*n). - _Vaclav Kotesovec_, Dec 05 2021

%o (PARI) a(n) = sum(k=0, n, k^(3*n));

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

%Y Cf. A249459, A349883, A349886.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 05 2021