A292305 - OEIS

%I #8 Sep 14 2017 08:16:36

%S 1,1,4,54,512,9375,186624,4117715,100663296,3099363912,100000000000,

%T 3423740047332,133741506723840,5451751918660554,244464150162276352,

%U 11823135040283203125,590295810358705651712,31435129951680797038726,1809934771463640728469504

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

%H Vaclav Kotesovec, <a href="/A292305/b292305.txt">Table of n, a(n) for n = 0..380</a>

%F a(n) = n^n * A000009(n).

%F a(n) ~ exp(Pi*sqrt(n/3)) * n^(n-3/4) / (4*3^(1/4)).

%t nmax = 20; Table[SeriesCoefficient[Product[(1+n^k*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

%t Flatten[{1, Table[n^n*PartitionsQ[n], {n, 1, 20}]}]

%Y Cf. A265949, A292190, A291698, A292306.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Sep 14 2017