A160987 Number of partitions of n where every part appears at least 17 times

0, 0, 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, 1, 1, 2, 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, 11, 10, 13, 13, 13, 14, 17, 15, 17, 18, 19, 19, 21, 20, 23, 23, 23, 24, 27, 28, 28, 30, 31, 32, 35, 34, 36, 38, 38, 40, 42, 42, 43, 45, 47, 47, 53, 51

Offset

1,34

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(-17*x)) dx = -1.324115652777071770633973742770277572729211213136860871177... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(17*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A066788 A160988 A184319 * A230773 A338732 A309026

Adjacent sequences: A160984 A160985 A160986 * A160988 A160989 A160990

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved