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A300975 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^3))^n.

%I A300975 #8 Mar 23 2018 05:31:34
%S A300975 1,1,3,10,35,126,462,1716,6443,24391,92928,355862,1368458,5280744,
%T A300975 20438148,79302960,308385355,1201536286,4689450021,18330233110,
%U A300975 71747534460,281177705490,1103163479190,4332522733560,17031238725410,67007449610751,263841039245280,1039628691988795
%N A300975 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^3))^n.
%C A300975 Number of partitions of n into cubes of n kinds.
%H A300975 Vaclav Kotesovec, <a href="/A300975/b300975.txt">Table of n, a(n) for n = 0..500</a>
%H A300975 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A300975 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A300975 a(n) ~ c * d^n / sqrt(n), where d = 4.0147940395164236614815683662796167488... and c = 0.2726202310726337579308600184572222... - _Vaclav Kotesovec_, Mar 23 2018
%p A300975 a:= proc(m) option remember; local b; b:= proc(n, i)
%p A300975       option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A300975       binomial(m+j-1, j)*b(n-i^3*j, i-1), j=0..n/i^3)))
%p A300975       end: b(n, iroot(n, 3))
%p A300975     end:
%p A300975 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 17 2018
%t A300975 Table[SeriesCoefficient[Product[1/(1 - x^k^3)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]
%Y A300975 Cf. A000578, A003108, A008485, A023872, A298434, A300974.
%K A300975 nonn
%O A300975 0,3
%A A300975 _Ilya Gutkovskiy_, Mar 17 2018