A160983 Number of partitions of n where every part appears at least 13 times

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, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 8, 7, 8, 9, 11, 10, 12, 12, 14, 14, 15, 15, 18, 17, 18, 19, 21, 23, 23, 24, 26, 27, 29, 29, 31, 32, 33, 35, 36, 37, 42, 41, 46, 46, 50, 51, 58, 58, 63, 63, 71, 71, 81, 83, 89, 92, 101, 104

Offset

1,26

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(-13*x)) dx = -1.268360284879056481996044472640421046229516947156436515845... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(13*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161088 A161304 A161279 * A322354 A336312 A161237

Adjacent sequences: A160980 A160981 A160982 * A160984 A160985 A160986

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved