A286352 - OEIS

%I #20 Feb 06 2018 11:45:45

%S 1,1,0,1,-1,0,1,-2,0,0,1,-3,1,-1,0,1,-4,3,-2,1,0,1,-5,6,-4,4,-1,0,1,

%T -6,10,-8,9,-4,1,0,1,-7,15,-15,17,-12,5,-1,0,1,-8,21,-26,30,-28,15,-6,

%U 2,0,1,-9,28,-42,51,-56,38,-21,9,-2,0,1,-10,36,-64,84

%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 + x^j)^k.

%H Seiichi Manyama, <a href="/A286352/b286352.txt">Antidiagonals n = 0..139, flattened</a>

%F G.f. of column k: Product_{j>=1} 1/(1 + x^j)^k.

%e Square array begins:

%e    1,  1,  1,  1,  1,   1, ...

%e    0, -1, -2, -3, -4,  -5, ...

%e    0,  0,  1,  3,  6,  10, ...

%e    0, -1, -2, -4, -8, -15, ...

%e    0,  1,  4,  9, 17,  30, ...

%Y Columns k=0-32 give: A000007, A081362, A022597-A022627.

%Y Main diagonal gives A255526.

%Y Antidiagonal sums give A299208.

%Y Cf. A286335.

%K sign,tabl

%O 0,8

%A _Seiichi Manyama_, May 08 2017