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%I #13 Jun 22 2023 07:21:03
%S 1,1,0,1,-1,0,1,-2,1,0,1,-3,3,-1,0,1,-4,6,-4,0,0,1,-5,10,-10,3,1,0,1,
%T -6,15,-20,12,0,-2,0,1,-7,21,-35,31,-9,-5,3,0,1,-8,28,-56,65,-36,-2,
%U 12,-3,0,1,-9,36,-84,120,-96,24,24,-18,1,0,1,-10,45,-120,203,-210,105,20,-54,18,2,0
%N Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^2))^k.
%F T(0,k) = 1; T(n,k) = -(k/n) * Sum_{j=1..n} A162552(j) * T(n-j,k).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 0, -1, -2, -3, -4, -5, -6, ...
%e 0, 1, 3, 6, 10, 15, 21, ...
%e 0, -1, -4, -10, -20, -35, -56, ...
%e 0, 0, 3, 12, 31, 65, 120, ...
%e 0, 1, 0, -9, -36, -96, -210, ...
%e 0, -2, -5, -2, 24, 105, 294, ...
%Y Columns k=0..3 give A000007, A317665, A363774, A363775.
%Y Main diagonal gives A363780.
%Y Cf. A045847, A162552, A363779.
%K sign,tabl
%O 0,8
%A _Seiichi Manyama_, Jun 21 2023
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