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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..380 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 Cf. A265949, A292190, A291698, A292306. Sequence in context: A208954 A269507 A302942 * A073863 A269480 A199022 Adjacent sequences: A292302 A292303 A292304 * A292306 A292307 A292308 KEYWORD nonn AUTHOR Vaclav Kotesovec, Sep 14 2017 STATUS approved

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Last modified September 13 08:33 EDT 2024. Contains 375902 sequences. (Running on oeis4.)