A292305 a(n) = [x^n] Product_{k>=1} (1 + n^k*x^k).

1, 1, 4, 54, 512, 9375, 186624, 4117715, 100663296, 3099363912, 100000000000, 3423740047332, 133741506723840, 5451751918660554, 244464150162276352, 11823135040283203125, 590295810358705651712, 31435129951680797038726, 1809934771463640728469504

Offset: 0

Author

Vaclav Kotesovec, Sep 14 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A265949, A292190, A291698, A292306.

Programs

Mathematica

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

Formula

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

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