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A160978 Number of partitions of n where every part appears at least 8 times 1

%I

%S 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,4,2,4,4,5,4,7,5,9,8,9,

%T 9,13,10,13,13,18,15,19,17,22,22,23,22,32,27,33,32,39,37,46,43,57,52,

%U 62,60,78,70,84,85,105,99,118,113,138,134,157,153,191,178,208,208,241,234,274,266,321,312

%N Number of partitions of n where every part appears at least 8 times

%H R. H. Hardin, <a href="/A160978/b160978.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(-8*x)) dx = -1.144792197520876814655151263033155873496440887922318876664... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(8*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,16

%A _R. H. Hardin_ Jun 01 2009

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Last modified September 23 15:23 EDT 2021. Contains 347618 sequences. (Running on oeis4.)