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