A160985 Number of partitions of n where every part appears at least 15 times

0, 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, 1, 2, 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, 9, 9, 13, 11, 12, 14, 15, 14, 17, 16, 18, 19, 19, 19, 23, 21, 22, 27, 26, 26, 29, 29, 32, 33, 32, 34, 38, 37, 37, 41, 41, 41, 49, 46, 50, 52, 54, 57, 65, 61, 67, 70, 77

Offset

1,30

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(-15*x)) dx = -1.299099673880548910845314768396583476528526604991203773132... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(15*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A287867 A023126 A329129 * A167968 A161239 A161063

Adjacent sequences: A160982 A160983 A160984 * A160986 A160987 A160988

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved