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A293908 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).

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