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A293718 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).

%I A293718 #25 Oct 16 2017 12:55:28
%S A293718 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 A293718 5,31,241,1181,1741,1,1,1,5,31,241,1661,9661,8485,1,1,1,5,31,241,2261,
%U A293718 16861,77155,57233,1,1,1,5,31,241,2261,20461,181315,794081
%N A293718 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 A293718 Seiichi Manyama, <a href="/A293718/b293718.txt">Antidiagonals n = 0..139, flattened</a>
%F A293718 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 A293718 Square array begins:
%e A293718    1,   1,    1,    1,    1, ...
%e A293718    1,   1,    1,    1,    1, ...
%e A293718    1,   5,    5,    5,    5, ...
%e A293718    1,  13,   31,   31,   31, ...
%e A293718    1,  73,  145,  241,  241, ...
%e A293718    1, 281, 1181, 1661, 2261, ...
%Y A293718 Columns k=1..4 give A000012, A115329, A293716, A293717.
%Y A293718 Rows n=0-1 give A000012.
%Y A293718 Main diagonal gives A082579.
%Y A293718 Cf. A293669, A293724.
%K A293718 nonn,tabl
%O A293718 0,9
%A A293718 _Seiichi Manyama_, Oct 15 2017