A160988 Number of partitions of n where every part appears at least 18 times

0, 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, 1, 2, 1, 2, 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, 10, 10, 11, 10, 15, 12, 14, 15, 17, 15, 19, 17, 20, 20, 21, 20, 25, 22, 24, 25, 27, 25, 32, 28, 32, 32, 34, 34, 39, 35, 39, 40, 43, 40, 46, 43, 47

Offset

1,36

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(-18*x)) dx = -1.334989118601880353022790449460912585887590533324376464199... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(18*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A322357 A160989 A066788 * A184319 A160987 A230773

Adjacent sequences: A160985 A160986 A160987 * A160989 A160990 A160991

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved