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A304629
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a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(5*k)))^n.
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2
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1, 1, 3, 13, 51, 201, 819, 3389, 14131, 59341, 250703, 1064207, 4535091, 19390229, 83139955, 357354213, 1539272499, 6642769925, 28714955571, 124312591469, 538895612751, 2338948779320, 10162837993377, 44202371860240, 192431323820851, 838442649862701, 3656031108325651
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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/(1 - x^k + x^(2*k) - x^(3*k) + x^(4*k))^n.
a(n) ~ c * d^n / sqrt(n), where d = 4.445766346387064439086120427... and c = 0.267035948020079842478290... - Vaclav Kotesovec, May 18 2018
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MATHEMATICA
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Table[SeriesCoefficient[Product[((1 + x^k)/(1 + x^(5 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[Product[1/(1 - x^k + x^(2 k) - x^(3 k) + x^(4 k))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
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CROSSREFS
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Cf. A096938, A255526, A285291, A296163, A296164, A304628.
Sequence in context: A101052 A016064 A163774 * A301458 A244784 A197074
Adjacent sequences: A304626 A304627 A304628 * A304630 A304631 A304632
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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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