A160986 - OEIS

%I #8 Jan 05 2016 12:08:03

%S 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,

%T 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,

%U 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

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

%H R. H. Hardin, <a href="/A160986/b160986.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(-16*x)) dx = -1.312209464445062445181826558955439962980138911918364832857... . - _Vaclav Kotesovec_, Jan 05 2016

%t 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 *)

%K nonn

%O 1,32

%A _R. H. Hardin_ Jun 01 2009