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A285243 Expansion of Product_{k>=1} 1/(1 - k*x^(k^2))^k. 4

%I

%S 1,1,1,1,5,5,5,5,17,26,26,26,58,94,94,94,190,298,352,352,608,896,1112,

%T 1112,1752,2641,3289,3559,5095,7499,9227,10307,14051,20111,25520,

%U 28760,38843,53467,68191,76831,102187,138283,175543,202813,263905,355220,445364

%N Expansion of Product_{k>=1} 1/(1 - k*x^(k^2))^k.

%H Vaclav Kotesovec, <a href="/A285243/b285243.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ c * n * 2^(n/4), where

%F c = 37.4093119651465404809069752821426852731608123... if mod(n,4)=0

%F c = 37.6275180026872367633343656570058911570800766... if mod(n,4)=1

%F c = 37.7650387085085950514850376086515488784106690... if mod(n,4)=2

%F c = 37.4702467422193571732026074780460498930830447... if mod(n,4)=3

%t nmax = 100; CoefficientList[Series[Product[1/(1 - k*x^(k^2))^k, {k,1,nmax}], {x,0,nmax}], x]

%Y Cf. A285047, A266941, A285241, A285242, A285245.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Apr 15 2017

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)