A160984 Number of partitions of n where every part appears at least 14 times

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, 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, 12, 11, 12, 12, 16, 13, 16, 16, 18, 17, 20, 18, 22, 21, 25, 23, 28, 25, 29, 30, 32, 30, 35, 33, 38, 36, 39, 38, 47, 43, 48, 48, 54, 52, 63, 58, 67, 65, 74, 73, 85, 79, 95

Offset

1,28

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(-14*x)) dx = -1.284573189673851723704615507462186169038822303924896813445... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(14*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161089 A161305 A161280 * A346094 A082898 A095999

Adjacent sequences: A160981 A160982 A160983 * A160985 A160986 A160987

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved