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A292304 a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k). 5
1, 1, 4, 90, 272, 1275, 49284, 124901, 536640, 1620648, 104040100, 223290012, 880969104, 2485978170, 7454471332, 592164776475, 1138401673472, 4109108002310, 10877348160900, 30962024560494, 72270337440400, 7523649856001916, 13202150810778116, 44577985082575400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Vaclav Kotesovec, Graph - The asymptotic ratio

FORMULA

Conjecture: a(n) ~ exp(2*sqrt((Pi^2/6 + 2*log(n)^2)*n)) * (Pi^2/6 + 2*log(n)^2)^(1/4) / (2 * sqrt(Pi) * n^(7/4)).

MATHEMATICA

nmax = 30; Table[SeriesCoefficient[Product[(1+n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

Table[SeriesCoefficient[QPochhammer[-n^2, x, 1 + n]/(1 + n^2), {x, 0, n}], {n, 0, 30}]

CROSSREFS

Cf. A092484, A291698.

Sequence in context: A220341 A184955 A205295 * A218385 A189882 A067767

Adjacent sequences:  A292301 A292302 A292303 * A292305 A292306 A292307

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 14 2017

STATUS

approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)