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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).
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%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