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A160978 Number of partitions of n where every part appears at least 8 times 1
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 9, 8, 9, 9, 13, 10, 13, 13, 18, 15, 19, 17, 22, 22, 23, 22, 32, 27, 33, 32, 39, 37, 46, 43, 57, 52, 62, 60, 78, 70, 84, 85, 105, 99, 118, 113, 138, 134, 157, 153, 191, 178, 208, 208, 241, 234, 274, 266, 321, 312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

LINKS

R. H. Hardin, Table of n, a(n) for n=1..1000

FORMULA

a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-8*x)) dx = -1.144792197520876814655151263033155873496440887922318876664... . - Vaclav Kotesovec, Jan 05 2016

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(8*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Sequence in context: A161083 A161299 A161274 * A231776 A055734 A295660

Adjacent sequences:  A160975 A160976 A160977 * A160979 A160980 A160981

KEYWORD

nonn

AUTHOR

R. H. Hardin Jun 01 2009

STATUS

approved

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Last modified July 30 16:31 EDT 2021. Contains 346359 sequences. (Running on oeis4.)