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A298641 Number of partitions of n^3 into cubes > 1.

%I A298641 #13 Jan 31 2018 08:29:15
%S A298641 1,0,1,1,2,1,8,6,45,100,377,1181,4063,13225,45218,150928,511970,
%T A298641 1717140,5777895,19308880,64360153,213446697,705095144,2317573307,
%U A298641 7583418322,24690176885,80003762726,257959340058,827713115396,2642967441892,8398644246488
%N A298641 Number of partitions of n^3 into cubes > 1.
%H A298641 Vaclav Kotesovec, <a href="/A298641/b298641.txt">Table of n, a(n) for n = 0..100</a>
%H A298641 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%H A298641 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A298641 a(n) = [x^(n^3)] Product_{k>=2} 1/(1 - x^(k^3)).
%F A298641 a(n) = A078128(A000578(n)).
%F A298641 a(n) ~ exp(4*(Gamma(1/3) * Zeta(4/3))^(3/4) * n^(3/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(3/2) / (8 * 3^(5/2) * Pi^2 * n^6). - _Vaclav Kotesovec_, Jan 31 2018
%e A298641 a(4) = 2 because we have [64] and [8, 8, 8, 8, 8, 8, 8, 8].
%p A298641 g:= proc(n, L) # number of partitions of n into cubes > 1 and <= L
%p A298641    option remember;
%p A298641    local t,k;
%p A298641    t:= 0;
%p A298641    if n = 0 then return 1 fi;
%p A298641    if n < 8 then return 0 fi;
%p A298641    for k from 2 while k^3 <= min(n,L) do
%p A298641      t:= t + procname(n-k^3, k^3)
%p A298641    od
%p A298641 end proc:
%p A298641 f:= n -> g(n^3, n^3):
%p A298641 map(f, [$0..50]); # _Robert Israel_, Jan 24 2018
%t A298641 mx = 30; s = Series[Product[1/(1 - x^(k^3)), {k, 2, mx}], {x, 0, mx^3}]; Table[ CoefficientList[s, x][[1 + n^3]], {n, 0, mx}] (* _Robert G. Wilson v_, Jan 24 2018 *)
%Y A298641 Cf. A000578, A003108, A030272, A078128, A092362, A259792, A279329, A280130, A290247.
%K A298641 nonn
%O A298641 0,5
%A A298641 _Ilya Gutkovskiy_, Jan 24 2018