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A293724 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^2*x^j).

%I A293724 #20 Oct 16 2017 12:55:17
%S A293724 1,1,1,1,1,1,1,1,9,1,1,1,9,25,1,1,1,9,79,241,1,1,1,9,79,457,1041,1,1,
%T A293724 1,9,79,841,5901,10681,1,1,1,9,79,841,7821,66841,60649,1,1,1,9,79,841,
%U A293724 10821,118681,720259,658785,1,1,1,9,79,841,10821,136681,1782019
%N A293724 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^2*x^j).
%H A293724 Seiichi Manyama, <a href="/A293724/b293724.txt">Antidiagonals n = 0..139, flattened</a>
%F A293724 A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k,n)} j^3*A(n-j,k)/(n-j)!.
%e A293724 Square array begins:
%e A293724    1,    1,    1,    1,     1, ...
%e A293724    1,    1,    1,    1,     1, ...
%e A293724    1,    9,    9,    9,     9, ...
%e A293724    1,   25,   79,   79,    79, ...
%e A293724    1,  241,  457,  841,   841, ...
%e A293724    1, 1041, 5901, 7821, 10821, ...
%Y A293724 Columns k=1..4 give A000012, A293720, A293721, A293723.
%Y A293724 Rows n=0-1 give A000012.
%Y A293724 Main diagonal gives A255807.
%Y A293724 Cf. A293669, A293718.
%K A293724 nonn,tabl
%O A293724 0,9
%A A293724 _Seiichi Manyama_, Oct 15 2017