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A382956 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{p prime} 1/(1 - x^p - y^p).

%I A382956 #12 Apr 10 2025 06:48:29
%S A382956 1,0,0,1,0,1,1,0,0,1,1,0,2,0,1,2,0,1,1,0,2,2,0,3,2,3,0,2,3,0,3,1,1,3,
%T A382956 0,3,3,0,5,3,6,3,5,0,3,4,0,6,4,4,4,4,6,0,4,5,0,8,4,11,8,11,4,8,0,5,6,
%U A382956 0,10,6,10,9,9,10,6,10,0,6,7,0,13,8,19,13,28,13,19,8,13,0,7
%N A382956 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{p prime} 1/(1 - x^p - y^p).
%H A382956 Seiichi Manyama, <a href="/A382956/b382956.txt">Antidiagonals n = 0..139, flattened</a>
%F A382956 A(n,k) = A(k,n).
%e A382956 Square array begins:
%e A382956   1, 0,  1, 1,  1,  2,  2,  3,   3,   4, ...
%e A382956   0, 0,  0, 0,  0,  0,  0,  0,   0,   0, ...
%e A382956   1, 0,  2, 1,  3,  3,  5,  6,   8,  10, ...
%e A382956   1, 0,  1, 2,  1,  3,  4,  4,   6,   8, ...
%e A382956   1, 0,  3, 1,  6,  4, 11, 10,  19,  20, ...
%e A382956   2, 0,  3, 3,  4,  8,  9, 13,  17,  22, ...
%e A382956   2, 0,  5, 4, 11,  9, 28, 20,  50,  50, ...
%e A382956   3, 0,  6, 4, 10, 13, 20, 28,  38,  51, ...
%e A382956   3, 0,  8, 6, 19, 17, 50, 38, 104,  92, ...
%e A382956   4, 0, 10, 8, 20, 22, 50, 51,  92, 122, ...
%Y A382956 Columns k=0..1 give A000607, A000004.
%Y A382956 Cf. A322210, A382955.
%K A382956 nonn,tabl
%O A382956 0,13
%A A382956 _Seiichi Manyama_, Apr 10 2025