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A270919 Coefficient of x^n in Product_{k>=1} ((1 + x^k) / (1 - x^k))^n. 17
1, 2, 12, 80, 552, 3912, 28224, 206208, 1520784, 11297546, 84413912, 633713808, 4776117216, 36115518376, 273868321536, 2081866609920, 15859616674336, 121046064563376, 925411686479820, 7085465166635440, 54323193841192752, 416993869451825424, 3204447137019290944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1118 (terms 0..500 from Vaclav Kotesovec)

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 7.862983395705905261519347909953827161057584... and c = 0.299856802806668079413694689903953367699319...

a(n) = [x^n] 1/theta_4(x)^n, where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Nov 03 2017

MATHEMATICA

Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^n, {k, 1, n}], {x, 0, n}], {n, 0, 25}]

Table[SeriesCoefficient[(QPochhammer[-1, x]/QPochhammer[x, x])^n, {x, 0, n}]/2^n, {n, 0, 25}]

CROSSREFS

Main diagonal of A288515.

Cf. A008485, A156616, A270913, A270923, A270924, A309986.

Sequence in context: A107632 A270775 A240836 * A082142 A069723 A063481

Adjacent sequences:  A270916 A270917 A270918 * A270920 A270921 A270922

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 25 2016

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)