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 A261452 Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(2*k-1). 6
 1, 2, 8, 24, 66, 176, 448, 1096, 2608, 6042, 13664, 30280, 65856, 140800, 296432, 615264, 1260306, 2550368, 5102616, 10101000, 19797344, 38439088, 73976160, 141179480, 267300752, 502283714, 937077808, 1736296304, 3196144032, 5846632656, 10631038400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A253289 and A255835. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 26. FORMULA a(n) ~ 2^(1/3) * (7*Zeta(3))^(1/18) * exp(1/6 - Pi^4/(672*Zeta(3)) - Pi^2 * n^(1/3)/(4*(7*Zeta(3))^(1/3)) + 3/2*(7*Zeta(3))^(1/3) * n^(2/3)) / (A^2 * sqrt(3) * n^(5/9)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. MATHEMATICA nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A156616, A261386, A005309, A261451, A261389. Sequence in context: A294458 A333186 A229136 * A225524 A293006 A018045 Adjacent sequences: A261449 A261450 A261451 * A261453 A261454 A261455 KEYWORD nonn AUTHOR Vaclav Kotesovec, Aug 19 2015 STATUS approved

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Last modified September 26 07:08 EDT 2023. Contains 365653 sequences. (Running on oeis4.)