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A293530 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. 1/Product_{j > 0, j mod k > 0} exp(x^j).

%I A293530 #20 Oct 13 2017 05:23:05
%S A293530 1,1,0,1,-1,0,1,-1,1,0,1,-1,-1,-7,0,1,-1,-1,5,25,0,1,-1,-1,-1,-23,
%T A293530 -181,0,1,-1,-1,-1,25,-41,1201,0,1,-1,-1,-1,1,-101,1111,-10291,0,1,-1,
%U A293530 -1,-1,1,139,-209,-6259,97777,0,1,-1,-1,-1,1,19,-569,251,-16015
%N A293530 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. 1/Product_{j > 0, j mod k > 0} exp(x^j).
%H A293530 Seiichi Manyama, <a href="/A293530/b293530.txt">Antidiagonals n = 0..139, flattened</a>
%F A293530 E.g.f. of column k: exp((Sum_{j=1..k-1} x^j)/(x^k - 1)).
%e A293530 Square array begins:
%e A293530    1,    1,   1,    1,   1, ...
%e A293530    0,   -1,  -1,   -1,  -1, ...
%e A293530    0,    1,  -1,   -1,  -1, ...
%e A293530    0,   -7,   5,   -1,  -1, ...
%e A293530    0,   25, -23,   25,   1, ...
%e A293530    0, -181, -41, -101, 139, ...
%Y A293530 Columns k=1..3 give A000007, A293532, A293533.
%Y A293530 Rows n=0 gives A000012.
%Y A293530 Main diagonal gives A293116.
%Y A293530 Cf. A293525.
%K A293530 sign,tabl
%O A293530 0,14
%A A293530 _Seiichi Manyama_, Oct 11 2017