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A304628 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(4*k)))^n. 2
1, 1, 3, 13, 47, 181, 729, 2948, 12031, 49540, 205153, 853546, 3565505, 14943839, 62810786, 264650683, 1117486463, 4727486583, 20032950744, 85017558081, 361289789377, 1537198394570, 6547611493822, 27917246924099, 119141276756545, 508884954441331, 2175284934712217, 9305217981192748 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

FORMULA

a(n) = [x^n] Product_{k>=1} ((1 - x^(8*k-4))/(1 - x^(2*k-1)))^n.

a(n) ~ c * d^n / sqrt(n), where d = 4.3582188263213968630940316689... and c = 0.266443662680498334500839... - Vaclav Kotesovec, May 18 2018

MATHEMATICA

Table[SeriesCoefficient[Product[((1 + x^k)/(1 + x^(4 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

Table[SeriesCoefficient[Product[((1 - x^(8 k - 4))/(1 - x^(2 k - 1)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

CROSSREFS

Cf. A070048, A255526, A285290, A296044, A296164, A304629.

Sequence in context: A089930 A228529 A084519 * A265920 A262322 A180278

Adjacent sequences:  A304625 A304626 A304627 * A304629 A304630 A304631

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 15 2018

STATUS

approved

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Last modified August 15 17:39 EDT 2022. Contains 356148 sequences. (Running on oeis4.)