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A283675 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^j)^(j^(k*j)) in powers of x. 5

%I

%S 1,1,-1,1,-1,-1,1,-1,-4,0,1,-1,-16,-23,0,1,-1,-64,-713,-223,1,1,-1,

%T -256,-19619,-64687,-2767,0,1,-1,-1024,-531185,-16755517,-9688545,

%U -42268,1,1,-1,-4096,-14347883,-4294403215,-30499543213,-2165715003,-759008,0,1,-1,-16384

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

%H Seiichi Manyama, <a href="/A283675/b283675.txt">Antidiagonals n = 0..52, flattened</a>

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

%F A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1)) * A(n-j,k) for n > 0. - _Seiichi Manyama_, Nov 04 2017

%e Square array begins:

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

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

%e -1, -4, -16, -64, ...

%e 0, -23, -713, -19619, ...

%e 0, -223, -64687, -16755517, ...

%Y Columns k=0..4 give A010815, A283499, A283534, A283536, A283803.

%Y Rows n=0..1 give A000012, (-1)*A000012.

%Y Main diagonal gives A283720.

%Y Cf. A283674.

%K sign,tabl

%O 0,9

%A _Seiichi Manyama_, Mar 14 2017

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Last modified October 13 19:35 EDT 2019. Contains 327981 sequences. (Running on oeis4.)