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A291697 a(n) = [x^n] Product_{k>=0} ((1 + x^(2*k+1))/(1 - x^(2*k+1)))^n. 3
1, 2, 8, 44, 256, 1512, 9056, 54896, 335872, 2069774, 12827888, 79875996, 499305472, 3131436856, 19694403520, 124165133424, 784478240768, 4965659813668, 31484486937512, 199923173603596, 1271192603065856, 8092551782518688, 51574780342740256, 329022223268286288, 2100934234342260736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A289522(n,n).

a(n) ~ c * d^n / sqrt(n), where d = 6.52085730573545526010335599231748172235904... and c = 0.296494808714349908707366708893... - Vaclav Kotesovec, Aug 30 2017

MATHEMATICA

Table[SeriesCoefficient[Product[((1 + x^(2 k + 1))/(1 - x^(2 k + 1)))^n, {k, 0, n}], {x, 0, n}], {n, 0, 24}]

Table[SeriesCoefficient[(QPochhammer[-x, x^2]/QPochhammer[x, x^2])^n, {x, 0, n}], {n, 0, 24}]

CROSSREFS

Main diagonal of A289522.

Cf. A270919.

Sequence in context: A192469 A128656 A208044 * A047851 A177260 A121747

Adjacent sequences:  A291694 A291695 A291696 * A291698 A291699 A291700

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 30 2017

STATUS

approved

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Last modified April 20 12:44 EDT 2021. Contains 343135 sequences. (Running on oeis4.)