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A293299 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} 1/(Sum_{j=0..k} x^(j*i)/j!).

%I A293299 #17 Oct 05 2017 11:22:13
%S A293299 1,1,0,1,-1,0,1,-1,0,0,1,-1,-1,-6,0,1,-1,-1,0,24,0,1,-1,-1,-1,-6,-120,
%T A293299 0,1,-1,-1,-1,2,30,720,0,1,-1,-1,-1,1,10,270,-5040,0,1,-1,-1,-1,1,20,
%U A293299 170,0,80640,0,1,-1,-1,-1,1,19,140,1050,2520,-725760,0,1,-1
%N A293299 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} 1/(Sum_{j=0..k} x^(j*i)/j!).
%H A293299 Seiichi Manyama, <a href="/A293299/b293299.txt">Antidiagonals n = 0..139, flattened</a>
%e A293299 Square array begins:
%e A293299    1,    1,  1,  1,  1, ...
%e A293299    0,   -1, -1, -1, -1, ...
%e A293299    0,    0, -1, -1, -1, ...
%e A293299    0,   -6,  0, -1, -1, ...
%e A293299    0,   24, -6,  2,  1, ...
%e A293299    0, -120, 30, 10, 20, ...
%Y A293299 Columns k=0..1 give A000007, A293300.
%Y A293299 Rows n=0 gives A000012.
%Y A293299 Main diagonal gives A293116.
%Y A293299 Cf. A293135, A293301.
%K A293299 sign,tabl
%O A293299 0,14
%A A293299 _Seiichi Manyama_, Oct 05 2017