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A294808 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j^(k*j)*x^j)^j in powers of x.

%I A294808 #21 Nov 18 2017 04:21:39
%S A294808 1,1,-1,1,-1,-2,1,-1,-8,-1,1,-1,-32,-73,0,1,-1,-128,-2155,-927,4,1,-1,
%T A294808 -512,-58921,-259701,-13969,4,1,-1,-2048,-1593811,-67045719,-48496253,
%U A294808 -254580,7,1,-1,-8192,-43044673,-17178209325,-152513227585,-13001952944,-5288596,3
%N A294808 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j^(k*j)*x^j)^j in powers of x.
%H A294808 Seiichi Manyama, <a href="/A294808/b294808.txt">Antidiagonals n = 0..52, flattened</a>
%F A294808 A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j)) * A(n-j,k) for n > 0.
%e A294808 Square array begins:
%e A294808     1,      1,         1,             1,                1, ...
%e A294808    -1,     -1,        -1,            -1,               -1, ...
%e A294808    -2,     -8,       -32,          -128,             -512, ...
%e A294808    -1,    -73,     -2155,        -58921,         -1593811, ...
%e A294808     0,   -927,   -259701,     -67045719,     -17178209325, ...
%e A294808     4, -13969, -48496253, -152513227585, -476819162106101, ...
%Y A294808 Columns k=0..2 give A073592, A294809, A294953.
%Y A294808 Rows n=0..2 give A000012, (-1)*A000012, (-1)*A004171.
%Y A294808 Cf. A294653, A294950.
%K A294808 sign,tabl
%O A294808 0,6
%A A294808 _Seiichi Manyama_, Nov 09 2017