A363779 - OEIS

%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