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A340983 Number of ways to write n as an ordered sum of 10 positive cubes.

%I A340983 #10 Feb 02 2021 20:06:13
%S A340983 1,0,0,0,0,0,0,10,0,0,0,0,0,0,45,0,0,0,0,0,0,120,0,0,0,0,10,0,210,0,0,
%T A340983 0,0,90,0,252,0,0,0,0,360,0,210,0,0,0,0,840,0,120,0,0,45,0,1260,0,45,
%U A340983 0,0,360,0,1260,0,20,0,0,1260,0,840,0,91,0,0,2520,0,360,0,360,120,0,3150,0,90
%N A340983 Number of ways to write n as an ordered sum of 10 positive cubes.
%H A340983 Robert Israel, <a href="/A340983/b340983.txt">Table of n, a(n) for n = 10..10000</a>
%H A340983 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A340983 G.f.: (Sum_{k>=1} x^(k^3))^10.
%p A340983 b:= proc(n, t) option remember;
%p A340983       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340983       `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
%p A340983     end:
%p A340983 a:= n-> b(n, 10):
%p A340983 seq(a(n), n=10..92);  # _Alois P. Heinz_, Feb 01 2021
%t A340983 nmax = 92; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
%Y A340983 Cf. A000578, A010057, A025463, A051344, A280618, A340977, A340978, A340979, A340980, A340981, A340982.
%K A340983 nonn,look
%O A340983 10,8
%A A340983 _Ilya Gutkovskiy_, Feb 01 2021