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

Author

R. H. Hardin Jun 01 2009

Keywords

• nonn

Links

• R. H. Hardin, Table of n, a(n) for n=1..1000

Programs

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 *)

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