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A304628
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a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(4*k)))^n.
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2
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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
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..500
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FORMULA
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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
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A070048, A255526, A285290, A296044, A296164, A304629.
Sequence in context: A089930 A228529 A084519 * A265920 A262322 A180278
Adjacent sequences: A304625 A304626 A304627 * A304629 A304630 A304631
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, May 15 2018
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STATUS
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approved
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