A160980 - OEIS

%I #8 Jan 05 2016 12:05:30

%S 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,

%T 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,

%U 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

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

%H R. H. Hardin, <a href="/A160980/b160980.txt">Table of n, a(n) for n=1..1000</a>

%F 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

%t 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 *)

%K nonn

%O 1,20

%A _R. H. Hardin_ Jun 01 2009