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A293785 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)*x^j).

%I A293785 #18 Oct 21 2017 15:42:13
%S A293785 1,1,1,1,1,2,1,1,3,6,1,1,5,13,24,1,1,9,31,73,120,1,1,17,79,241,501,
%T A293785 720,1,1,33,211,841,2261,4051,5040,1,1,65,583,3049,10821,24781,37633,
%U A293785 40320,1,1,129,1651,11353,54221,162601,309835,394353,362880,1,1,257
%N A293785 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)*x^j).
%H A293785 Seiichi Manyama, <a href="/A293785/b293785.txt">Antidiagonals n = 0..139, flattened</a>
%F A293785 A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j^k*A(n-j,k)/(n-j)! for n > 0.
%e A293785 Square array begins:
%e A293785      1,   1,    1,     1,     1, ...
%e A293785      1,   1,    1,     1,     1, ...
%e A293785      2,   3,    5,     9,    17, ...
%e A293785      6,  13,   31,    79,   211, ...
%e A293785     24,  73,  241,   841,  3049, ...
%e A293785    120, 501, 2261, 10821, 54221, ...
%Y A293785 Columns k=0..4 give A000142, A000262, A082579, A255807, A255819.
%Y A293785 Rows n=0-1 give A000012.
%Y A293785 Main diagonal gives A293786.
%K A293785 nonn,tabl
%O A293785 0,6
%A A293785 _Seiichi Manyama_, Oct 16 2017