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Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} j*x^j).
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%I #25 Oct 16 2017 12:55:28

%S 1,1,1,1,1,1,1,1,5,1,1,1,5,13,1,1,1,5,31,73,1,1,1,5,31,145,281,1,1,1,

%T 5,31,241,1181,1741,1,1,1,5,31,241,1661,9661,8485,1,1,1,5,31,241,2261,

%U 16861,77155,57233,1,1,1,5,31,241,2261,20461,181315,794081

%N Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} j*x^j).

%H Seiichi Manyama, <a href="/A293718/b293718.txt">Antidiagonals n = 0..139, flattened</a>

%F A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k,n)} j^2*A(n-j,k)/(n-j)!.

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 1, 1, 1, 1, 1, ...

%e 1, 5, 5, 5, 5, ...

%e 1, 13, 31, 31, 31, ...

%e 1, 73, 145, 241, 241, ...

%e 1, 281, 1181, 1661, 2261, ...

%Y Columns k=1..4 give A000012, A115329, A293716, A293717.

%Y Rows n=0-1 give A000012.

%Y Main diagonal gives A082579.

%Y Cf. A293669, A293724.

%K nonn,tabl

%O 0,9

%A _Seiichi Manyama_, Oct 15 2017