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A160979 Number of partitions of n where every part appears at least 9 times 1
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 10, 8, 9, 11, 12, 11, 14, 13, 15, 19, 17, 18, 22, 21, 23, 25, 25, 26, 33, 31, 34, 37, 39, 40, 50, 46, 52, 59, 62, 65, 75, 74, 82, 89, 98, 98, 118, 115, 128, 138, 147, 153, 173, 174, 194, 208, 220, 228, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,18

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(-9*x)) dx = -1.177746328175383925002682189470669316299189793135604988217... . - Vaclav Kotesovec, Jan 05 2016

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(9*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Sequence in context: A161084 A161300 A161275 * A323287 A167679 A051881

Adjacent sequences:  A160976 A160977 A160978 * A160980 A160981 A160982

KEYWORD

nonn

AUTHOR

R. H. Hardin Jun 01 2009

STATUS

approved

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Last modified July 30 03:53 EDT 2021. Contains 346347 sequences. (Running on oeis4.)