%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