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%I #18 Dec 30 2016 16:02:48
%S 1,0,1,1,2,2,4,4,6,8,11,13,19,22,30,37,48,58,76,91,116,141,176,212,
%T 265,317,390,468,571,681,828,983,1185,1407,1685,1993,2378,2802,3326,
%U 3913,4624,5421,6387,7466,8762,10223,11955,13910,16225,18831,21898,25365
%N Number of partitions of n having no perfect cube parts (n>=0).
%C a(n) = A264391(n,0).
%C Convolution of A279484 and A000041. - _Vaclav Kotesovec_, Dec 30 2016
%H Vaclav Kotesovec, <a href="/A264393/b264393.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{i>=1}(1-x^(h(i)))/(1-x^i), where h(i) = i^3.
%F a(n) ~ exp(Pi*sqrt(2*n/3) - 2^(1/6) * Gamma(1/3) * Zeta(4/3) * n^(1/6) / (3^(5/6) * Pi^(1/3))) * Pi / (6^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Dec 30 2016
%e a(7) = 4 because we have [7], [5,2], [4,3], and [3,2,2].
%p h := proc (i) options operator, arrow; i^3 end proc: g := product((1-x^h(i))/(1-x^i), i = 1 .. 150): gser := series(g, x = 0, 65): seq(coeff(gser, x, n), n = 0 .. 60);
%t nmax=100; CoefficientList[Series[Product[(1-x^(k^3))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 30 2016 *)
%Y Cf. A264391, A279484.
%K nonn
%O 0,5
%A _Emeric Deutsch_, Nov 13 2015
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