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%I #16 Jun 22 2023 07:20:55
%S 1,1,0,1,-1,0,1,-2,1,0,1,-3,3,-1,0,1,-4,6,-4,1,0,1,-5,10,-10,5,-1,0,1,
%T -6,15,-20,15,-6,1,0,1,-7,21,-35,35,-21,7,-1,0,1,-8,28,-56,70,-56,28,
%U -8,0,0,1,-9,36,-84,126,-126,84,-36,7,1,0,1,-10,45,-120,210,-252,210,-120,42,-4,-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^3))^k.
%F T(0,k) = 1; T(n,k) = -(k/n) * Sum_{j=1..n} A363783(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, 1, 5, 15, 35, 70, 126, ...
%e 0, -1, -6, -21, -56, -126, -252, ...
%e 0, 1, 7, 28, 84, 210, 462, ...
%Y Columns k=0..3 give A000007, A323633, A363776, A363777.
%Y Main diagonal gives A363781.
%Y Cf. A290054, A363778, A363783.
%K sign,tabl
%O 0,8
%A _Seiichi Manyama_, Jun 21 2023