A160980 Number of partitions of n where every part appears at least 10 times

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 7, 7, 10, 8, 11, 10, 13, 12, 14, 13, 17, 15, 20, 18, 22, 20, 24, 24, 27, 25, 29, 28, 37, 32, 38, 37, 44, 43, 51, 48, 57, 54, 70, 64, 78, 73, 87, 86, 101, 98, 114, 110, 136, 127, 150, 146, 171, 168, 192

Offset

1,20

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(-10*x)) dx = -1.205537253124053741421631447140430212861580981956591015349... . - Vaclav Kotesovec, Jan 05 2016

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(10*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161085 A161301 A161276 * A065031 A305832 A058061

Adjacent sequences: A160977 A160978 A160979 * A160981 A160982 A160983

Keyword

nonn

Author

R. H. Hardin Jun 01 2009

Status

approved