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A160988 Number of partitions of n where every part appears at least 18 times 1

%I

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

%T 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,4,2,4,4,5,4,7,5,7,7,8,7,10,8,

%U 10,10,11,10,15,12,14,15,17,15,19,17,20,20,21,20,25,22,24,25,27,25,32,28,32,32,34,34,39,35,39,40,43,40,46,43,47

%N Number of partitions of n where every part appears at least 18 times

%H R. H. Hardin, <a href="/A160988/b160988.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(-18*x)) dx = -1.334989118601880353022790449460912585887590533324376464199... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(18*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,36

%A _R. H. Hardin_ Jun 01 2009

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Last modified December 3 20:35 EST 2021. Contains 349468 sequences. (Running on oeis4.)