cp's OEIS Frontend

A294951 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(-Sum_{j>=1} sigma_k(j) * x^j).

%I A294951 #14 Nov 13 2017 13:27:11
%S A294951 1,1,-1,1,-1,-3,1,-1,-5,-1,1,-1,-9,-7,1,1,-1,-17,-31,1,279,1,-1,-33,
%T A294951 -115,-23,839,301,1,-1,-65,-391,-215,3399,4171,12263,1,-1,-129,-1267,
%U A294951 -1319,17519,41311,54305,5601,1,-1,-257,-3991,-6839,102999,387031,473129,102817,-431281
%N A294951 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(-Sum_{j>=1} sigma_k(j) * x^j).
%F A294951 A(0,k) = 1 and A(n,k) = -(n-1)! * Sum_{j=1..n} j*sigma_k(j)*A(n-j,k)/(n-j)! for n > 0.
%e A294951 Square array A(n,k) begins:
%e A294951      1,   1,    1,     1,      1, ...
%e A294951     -1,  -1,   -1,    -1,     -1, ...
%e A294951     -3,  -5,   -9,   -17,    -33, ...
%e A294951     -1,  -7,  -31,  -115,   -391, ...
%e A294951      1,   1,  -23,  -215,  -1319, ...
%e A294951    279, 839, 3399, 17519, 102999, ...
%Y A294951 Columns k=0..2 give A294402, A294403, A294404.
%Y A294951 Rows n=0..2 give A000012, (-1)*A000012, (-1)*A000051(n+1).
%Y A294951 Cf. A294947.
%K A294951 sign,tabl
%O A294951 0,6
%A A294951 _Seiichi Manyama_, Nov 12 2017