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A294296 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 A294296 #30 Oct 31 2017 06:31:52
%S A294296 1,1,1,1,1,5,1,1,7,25,1,1,11,43,193,1,1,19,91,409,1481,1,1,35,223,
%T A294296 1105,3841,16021,1,1,67,595,3505,13841,50431,167665,1,1,131,1663,
%U A294296 12193,60841,230731,648187,2220065,1,1,259,4771,44689,297761,1340851,3955771
%N A294296 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).
%H A294296 Seiichi Manyama, <a href="/A294296/b294296.txt">Antidiagonals n = 0..139, flattened</a>
%F A294296 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 A294296 Square array A(n,k) begins:
%e A294296       1,    1,     1,     1,      1, ...
%e A294296       1,    1,     1,     1,      1, ...
%e A294296       5,    7,    11,    19,     35, ...
%e A294296      25,   43,    91,   223,    595, ...
%e A294296     193,  409,  1105,  3505,  12193, ...
%e A294296    1481, 3841, 13841, 60841, 297761, ...
%Y A294296 Columns k=0..2 give A294363, A294361, A294362.
%Y A294296 Rows n=0-1 give A000012.
%Y A294296 Main diagonal gives A294388.
%Y A294296 Cf. A144048.
%K A294296 nonn,tabl
%O A294296 0,6
%A A294296 _Seiichi Manyama_, Oct 30 2017