Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Oct 21 2017 15:42:13
%S 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 720,1,1,33,211,841,2261,4051,5040,1,1,65,583,3049,10821,24781,37633,
%U 40320,1,1,129,1651,11353,54221,162601,309835,394353,362880,1,1,257
%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)*x^j).
%H Seiichi Manyama, <a href="/A293785/b293785.txt">Antidiagonals n = 0..139, flattened</a>
%F 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 Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, ...
%e 2, 3, 5, 9, 17, ...
%e 6, 13, 31, 79, 211, ...
%e 24, 73, 241, 841, 3049, ...
%e 120, 501, 2261, 10821, 54221, ...
%Y Columns k=0..4 give A000142, A000262, A082579, A255807, A255819.
%Y Rows n=0-1 give A000012.
%Y Main diagonal gives A293786.
%K nonn,tabl
%O 0,6
%A _Seiichi Manyama_, Oct 16 2017