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A265840 Expansion of Product_{k>=1} (1 + k^3*x^k). 6
1, 1, 8, 35, 91, 405, 1069, 3799, 8686, 36744, 86310, 235776, 686329, 1605779, 5230579, 13191702, 30608501, 73907925, 206052723, 433747560, 1324608945, 2995740974, 6973434054, 15364943439, 35816669079, 86662644756, 184871083828, 502089539734, 1098571699830 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

FORMULA

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(3*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018

Conjecture: log(a(n)) ~ 3*sqrt(n/2) * (log(2*n) - 2). - Vaclav Kotesovec, Dec 27 2020

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1 + k^3*x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A022629, A092484, A265837, A265841, A265842.

Sequence in context: A305672 A100907 A303383 * A212903 A168566 A058102

Adjacent sequences:  A265837 A265838 A265839 * A265841 A265842 A265843

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 16 2015

STATUS

approved

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Last modified June 24 07:28 EDT 2021. Contains 345416 sequences. (Running on oeis4.)