A160985 - OEIS

%I #8 Jan 05 2016 12:07:34

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,

%T 1,2,1,2,1,2,1,2,1,2,3,3,3,5,4,5,6,6,6,8,7,8,9,9,9,13,11,12,14,15,14,

%U 17,16,18,19,19,19,23,21,22,27,26,26,29,29,32,33,32,34,38,37,37,41,41,41,49,46,50,52,54,57,65,61,67,70,77

%N Number of partitions of n where every part appears at least 15 times

%H R. H. Hardin, <a href="/A160985/b160985.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(-15*x)) dx = -1.299099673880548910845314768396583476528526604991203773132... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(15*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,30

%A _R. H. Hardin_ Jun 01 2009