A160979 Number of partitions of n where every part appears at least 9 times

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

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