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A035528 Euler transform of A027656(n-1). 23
0, 1, 1, 3, 3, 6, 9, 13, 19, 28, 42, 57, 84, 115, 164, 227, 313, 429, 588, 799, 1079, 1461, 1952, 2617, 3480, 4627, 6111, 8072, 10604, 13905, 18181, 23701, 30828, 39990, 51763, 66822, 86124, 110687, 142039, 181841, 232409, 296401, 377419 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) ~ A^(1/2) * Zeta(3)^(11/72) * exp(-1/24 - Pi^4/(1728*Zeta(3)) + Pi^2 * n^(1/3)/(3*2^(8/3)*Zeta(3)^(1/3)) +  3*Zeta(3)^(1/3) * n^(2/3)/2^(4/3)) / (sqrt(3*Pi) * 2^(71/72) * n^(47/72)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Oct 02 2015

MATHEMATICA

nmax = 50; CoefficientList[Series[-1 + Product[1/(1 - x^(2*k-1))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 19 2015 *)

nmax = 100; Flatten[{0, Rest[CoefficientList[Series[E^Sum[1/j*x^j/(1 - x^(2*j))^2, {j, 1, nmax}], {x, 0, nmax}], x]]}] (* Vaclav Kotesovec, Oct 10 2015 *)

CROSSREFS

Cf. A000219, A052847, A263150, A263352, A262876, A263136, A263141.

Sequence in context: A289143 A280240 A058628 * A300300 A293675 A050337

Adjacent sequences:  A035525 A035526 A035527 * A035529 A035530 A035531

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified January 21 17:38 EST 2019. Contains 319350 sequences. (Running on oeis4.)