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A261736 Expansion of Product_{k>=1} (1 + x^(6*k))/(1 + x^k). 11
1, -1, 0, -1, 1, -1, 2, -2, 2, -3, 3, -3, 5, -5, 5, -7, 8, -8, 11, -12, 12, -16, 17, -18, 23, -25, 26, -32, 35, -37, 45, -49, 52, -62, 67, -72, 85, -92, 98, -114, 124, -133, 153, -166, 178, -203, 220, -236, 268, -290, 311, -350, 379, -407, 456, -493, 529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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. 14.

FORMULA

a(n) ~ (-1)^n * exp(sqrt(2*n)*Pi/3) / (2^(7/4)*sqrt(3)*n^(3/4)).

MAPLE

seq(coeff(series(mul((1+x^(6*k))/(1+x^k), k=1..n), x, n+1), x, n), n=0..60); # Muniru A Asiru, Jul 29 2018

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[(1 + x^(6*k))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A081360 (m=2), A109389 (m=3), A261734 (m=4), A133563 (m=5), A113297 (m=7), A261735 (m=8), A261733 (m=9), A145707 (m=10).

Sequence in context: A062051 A179269 A108711 * A247049 A029059 A035449

Adjacent sequences:  A261733 A261734 A261735 * A261737 A261738 A261739

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Aug 30 2015

STATUS

approved

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Last modified November 16 21:47 EST 2018. Contains 317275 sequences. (Running on oeis4.)