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A292305
a(n) = [x^n] Product_{k>=1} (1 + n^k*x^k).
6
1, 1, 4, 54, 512, 9375, 186624, 4117715, 100663296, 3099363912, 100000000000, 3423740047332, 133741506723840, 5451751918660554, 244464150162276352, 11823135040283203125, 590295810358705651712, 31435129951680797038726, 1809934771463640728469504
OFFSET
0,3
LINKS
FORMULA
a(n) = n^n * A000009(n).
a(n) ~ exp(Pi*sqrt(n/3)) * n^(n-3/4) / (4*3^(1/4)).
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}]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 14 2017
STATUS
approved