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%I #19 Sep 23 2017 03:41:21
%S 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0
%N Number of partitions of n into distinct odd cubes.
%C In general, if m > 0 and g.f. = Product_{k>=1} (1 + x^((2*k-1)^m)), then a(n) ~ exp((m+1) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m) / m^2)^(m/(m+1)) * n^(1/(m+1)) / 2) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m))^(m/(2*(m+1))) / (2*sqrt(Pi*(m+1)) * m^((m-1)/(2*(m+1))) * n^((2*m+1)/(2*(m+1)))).
%H Vaclav Kotesovec, <a href="/A292547/b292547.txt">Table of n, a(n) for n = 0..100000</a>
%H Vaclav Kotesovec, <a href="/A292547/a292547.jpg">Graph - The asymptotic ratio</a>
%F G.f.: Product_{k>=1} (1 + x^((2*k-1)^3)).
%F a(n) ~ exp(2 * 3^(-3/2) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4)) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/8) / (4*3^(1/4) * sqrt(Pi) * n^(7/8)).
%t nmax = 200; CoefficientList[Series[Product[1 + x^((2*k-1)^3), {k, 1, Floor[nmax^(1/3)/2] + 1}], {x, 0, nmax}], x]
%Y Cf. A000700 (m=1), A167700 (m=2).
%Y Cf. A033461, A279329, A287091, A290276, A292740.
%K nonn
%O 0
%A _Vaclav Kotesovec_, Sep 18 2017
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