A292306 - OEIS

%I #7 Aug 22 2018 06:57:42

%S 1,1,4,756,65792,19534375,101564310279744,558547898753326097,

%T 9444733810164237336576,174449211609498720646587480,

%U 10000000004000000000400000000010000000000,6626407607852766876000106671521201448502431912

%N a(n) = [x^n] Product_{k>=1} (1 + n^n*x^k).

%H Vaclav Kotesovec, <a href="/A292306/b292306.txt">Table of n, a(n) for n = 0..56</a>

%F Conjecture: log(a(n)) ~ (sqrt(2)*n^(3/2) - n/2)*log(n). - _Vaclav Kotesovec_, Aug 22 2018

%t nmax = 14; Table[SeriesCoefficient[Product[(1+n^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

%Y Cf. A265949, A292190, A292305.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Sep 14 2017