A160978 Number of partitions of n where every part appears at least 8 times

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 9, 8, 9, 9, 13, 10, 13, 13, 18, 15, 19, 17, 22, 22, 23, 22, 32, 27, 33, 32, 39, 37, 46, 43, 57, 52, 62, 60, 78, 70, 84, 85, 105, 99, 118, 113, 138, 134, 157, 153, 191, 178, 208, 208, 241, 234, 274, 266, 321, 312

Offset

1,16

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(-8*x)) dx = -1.144792197520876814655151263033155873496440887922318876664... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(8*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161083 A161299 A161274 * A231776 A055734 A295660

Adjacent sequences: A160975 A160976 A160977 * A160979 A160980 A160981

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved