A293785 - OEIS

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 #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 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