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A290054 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j^3))^k.

%I A290054 #15 Apr 01 2018 05:53:01
%S A290054 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,4,3,0,0,0,1,5,6,1,0,0,0,1,6,10,4,0,0,
%T A290054 0,0,1,7,15,10,1,0,0,0,0,1,8,21,20,5,0,0,0,1,0,1,9,28,35,15,1,0,0,2,0,
%U A290054 0,1,10,36,56,35,6,0,0,3,2,0,0,1,11,45,84,70,21,1,0,4,6,0,0,0
%N A290054 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j^3))^k.
%C A290054 A(n,k) is the number of ways of writing n as a sum of k nonnegative cubes.
%H A290054 Seiichi Manyama, <a href="/A290054/b290054.txt">Antidiagonals n = 0..139, flattened</a>
%H A290054 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A290054 G.f. of column k: (Sum_{j>=0} x^(j^3))^k.
%e A290054 Square array begins:
%e A290054 1,  1,  1,  1,  1,   1,  ...
%e A290054 0,  1,  2,  3,  4,   5,  ...
%e A290054 0,  0,  1,  3,  6,  10,  ...
%e A290054 0,  0,  0,  1,  4,  10,  ...
%e A290054 0,  0,  0,  0,  1,   5,  ...
%e A290054 0,  0,  0,  0,  0,   1,  ...
%t A290054 Table[Function[k, SeriesCoefficient[Sum[x^i^3, {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
%Y A290054 Columns k=0-9 give: A000007, A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.
%Y A290054 Main diagonal gives A291700.
%Y A290054 Antidiagonal sums give A302019.
%Y A290054 Cf. A045847, A122141, A286815.
%K A290054 nonn,tabl
%O A290054 0,8
%A A290054 _Ilya Gutkovskiy_, Jul 19 2017