A160986 Number of partitions of n where every part appears at least 16 times

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, 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, 13, 11, 14, 13, 16, 15, 17, 16, 20, 18, 20, 20, 23, 21, 24, 23, 29, 26, 29, 28, 33, 32, 34, 33, 38, 36, 40, 38, 43, 41, 44, 44, 52, 48, 53, 52, 61, 58

Offset

1,32

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(-16*x)) dx = -1.312209464445062445181826558955439962980138911918364832857... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(16*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A230773 A338732 A309026 * A287867 A023126 A329129

Adjacent sequences: A160983 A160984 A160985 * A160987 A160988 A160989

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved