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A280662 G.f.: Product_{k>=1, j>=1} 1/(1 - x^(j*k^4)). 4

%I

%S 1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,232,298,387,493,632,799,

%T 1013,1270,1597,1988,2478,3066,3795,4666,5739,7018,8582,10442,12699,

%U 15379,18614,22443,27039,32470,38957,46601,55694,66383,79047,93901,111432

%N G.f.: Product_{k>=1, j>=1} 1/(1 - x^(j*k^4)).

%C In general, if m>=3 and g.f. = Product_{k>=1, j>=1} 1/(1-x^(j*k^m)), then a(n, m) ~ exp(Pi*sqrt(2*Zeta(m)*n/3) + Pi^(-1/m) * Gamma(1+1/m) * Zeta(1+1/m) * Zeta(1/m) * (6*n/Zeta(m))^(1/(2*m))) * 2^(m/4 - 7/8) * Pi^(m/4) * Zeta(m)^(1/8) / (3^(1/8) * n^(5/8)).

%H Vaclav Kotesovec, <a href="/A280662/b280662.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi^3 * sqrt(n/15)/3 + 2^(-7/4) * 3^(3/8) * 5^(1/8) * Pi^(-3/4) * Gamma(1/4) * Zeta(5/4) * Zeta(1/4) * n^(1/8)) * Pi^(3/2) / (3^(3/8) * 5^(1/8) * n^(5/8)).

%t nmax = 100; CoefficientList[Series[1/Product[1-x^(j*k^4), {k, 1, Floor[nmax^(1/4)]+1}, {j, 1, Floor[nmax/k^4]+1}], {x, 0, nmax}], x]

%Y Cf. A006171 (m=1), A004101 (m=2), A280661 (m=3).

%Y Cf. A280664.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 07 2017

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)