%I #12 Oct 21 2017 09:43:48
%S 1,1,1,1,1,2,1,1,3,8,1,1,5,19,38,1,1,9,49,121,238,1,1,17,133,409,1041,
%T 1828,1,1,33,373,1441,4841,10651,16096,1,1,65,1069,5233,23601,66541,
%U 121843,160604,1,1,129,3109,19441,119441,442681,1006825,1575729,1826684,1,1
%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} j^(k-1)*A000009(j)*x^j).
%H Seiichi Manyama, <a href="/A293908/b293908.txt">Antidiagonals n = 0..139, flattened</a>
%F A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j^k*A000009(j)*A(n-j,k)/(n-j)! for n > 0.
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, ...
%e 2, 3, 5, 9, 17, ...
%e 8, 19, 49, 133, 373, ...
%e 38, 121, 409, 1411, 5233, ...
%e 238, 1041, 4841, 23601, 119441, ...
%Y Columns k=0..2 give A293839, A293840, A293841.
%Y Rows n=0-1 give A000012.
%Y Cf. A293796.
%K nonn,tabl
%O 0,6
%A _Seiichi Manyama_, Oct 19 2017