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A160988 Number of partitions of n where every part appears at least 18 times 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 7, 7, 8, 7, 10, 8, 10, 10, 11, 10, 15, 12, 14, 15, 17, 15, 19, 17, 20, 20, 21, 20, 25, 22, 24, 25, 27, 25, 32, 28, 32, 32, 34, 34, 39, 35, 39, 40, 43, 40, 46, 43, 47 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,36

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(-18*x)) dx = -1.334989118601880353022790449460912585887590533324376464199... . - Vaclav Kotesovec, Jan 05 2016

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(18*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Sequence in context: A322357 A160989 A066788 * A184319 A160987 A230773

Adjacent sequences:  A160985 A160986 A160987 * A160989 A160990 A160991

KEYWORD

nonn

AUTHOR

R. H. Hardin Jun 01 2009

STATUS

approved

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Last modified October 21 11:09 EDT 2021. Contains 348150 sequences. (Running on oeis4.)