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A266648 Expansion of Product_{k>=1} (1 + x^(3*k)) / (1 - x^k). 10
1, 1, 2, 4, 6, 9, 15, 21, 31, 46, 64, 89, 126, 170, 231, 314, 417, 552, 733, 955, 1244, 1617, 2079, 2665, 3413, 4331, 5485, 6931, 8704, 10901, 13629, 16949, 21033, 26045, 32123, 39529, 48553, 59429, 72599, 88518, 107624, 130599, 158209, 191175, 230611, 277717, 333730, 400375, 479598, 573386, 684481 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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) ~ sqrt(7) * exp(sqrt(7*n)*Pi/3) / (24*n).

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1+x^(3*k))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000726, A015128, A100405, A266647, A266649, A266650, A285445, A285447.

Sequence in context: A323432 A327046 A024787 * A076922 A157679 A057602

Adjacent sequences:  A266645 A266646 A266647 * A266649 A266650 A266651

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 02 2016

STATUS

approved

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Last modified July 6 03:02 EDT 2020. Contains 335475 sequences. (Running on oeis4.)