login
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)^(j*k) in powers of x.
6

%I #23 Feb 06 2018 11:46:05

%S 1,1,0,1,-1,0,1,-2,-1,0,1,-3,-1,-2,0,1,-4,0,-2,1,0,1,-5,2,-1,7,0,0,1,

%T -6,5,0,15,2,4,0,1,-7,9,0,23,-3,10,2,0,1,-8,14,-2,30,-20,8,-8,8,0,1,

%U -9,20,-7,36,-51,2,-42,5,-2,0,1,-10,27,-16,42,-96,5,-88,6

%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)^(j*k) in powers of x.

%H Seiichi Manyama, <a href="/A279928/b279928.txt">Antidiagonals n = 0..139, flattened</a>

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

%e Square array begins:

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

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

%e 0, -1, -1, 0, 2, ...

%e 0, -2, -2, -1, 0, ...

%e 0, 1, 7, 15, 23, ...

%Y Columns k=0-5 give: A000007, A255528, A278710, A279031, A279411, A279932.

%Y Main diagonal gives A281266.

%Y Antidiagonal sums give A299212.

%Y Cf. A255961, A277938.

%K sign,tabl

%O 0,8

%A _Seiichi Manyama_, Apr 11 2017