A160981 Number of partitions of n where every part appears at least 11 times

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 8, 7, 10, 10, 10, 11, 14, 12, 14, 15, 16, 16, 18, 20, 21, 22, 22, 24, 28, 26, 27, 30, 31, 32, 37, 36, 40, 41, 45, 46, 54, 51, 57, 60, 66, 70, 77, 77, 87, 90, 97, 101, 115, 114, 125, 130, 146, 148

Offset

1,22

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(-11*x)) dx = -1.229377080445846476290496623787767636516770068349094281505... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(11*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161086 A161302 A161277 * A058656 A184221 A226898

Adjacent sequences: A160978 A160979 A160980 * A160982 A160983 A160984

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved