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A304629 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(5*k)))^n. 2
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 (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/(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

MATHEMATICA

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}]

CROSSREFS

Cf. A096938, A255526, A285291, A296163, A296164, A304628.

Sequence in context: A101052 A016064 A163774 * A301458 A244784 A197074

Adjacent sequences:  A304626 A304627 A304628 * A304630 A304631 A304632

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 15 2018

STATUS

approved

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Last modified May 23 03:10 EDT 2019. Contains 323507 sequences. (Running on oeis4.)