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A304461 Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^3). 0
1, 2, 144, 29232, 12263552, 8807437800, 9671073636672, 15075101792958592, 31660212257148109824, 86182291753025176234602, 295133367252867736074882400, 1241742977667269060006125955952, 6296492342467004634980003629748736, 37869525230334631809014462278624137096 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, for m>=3, coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^m) is asymptotic to 2^n * n^(m*n) / n!.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) ~ 2^(n - 1/2) * exp(n) * n^(2*n - 1/2) / sqrt(Pi).

MATHEMATICA

nmax = 20; Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^(n^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2/QPochhammer[x])^(n^3), {x, 0, n}], {n, 0, nmax}]

CROSSREFS

Cf. A206623, A270919, A304448, A304459, A304460.

Sequence in context: A282296 A163275 A157073 * A264153 A232998 A103207

Adjacent sequences:  A304458 A304459 A304460 * A304462 A304463 A304464

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 13 2018

STATUS

approved

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Last modified January 20 04:53 EST 2021. Contains 340301 sequences. (Running on oeis4.)