A293796 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)*A000041(j)*x^j).

1, 1, 1, 1, 1, 3, 1, 1, 5, 13, 1, 1, 9, 31, 79, 1, 1, 17, 79, 265, 579, 1, 1, 33, 211, 937, 2621, 5209, 1, 1, 65, 583, 3433, 12501, 31621, 53347, 1, 1, 129, 1651, 12889, 62141, 204361, 426595, 628257, 1, 1, 257, 4759, 49225, 319461, 1395121, 3703099

Offset

0,6

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Formula

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j^k*A000041(j)*A(n-j,k)/(n-j)! for n > 0.

Example

Square array begins:
     1,    1,     1,     1,      1, ...
     1,    1,     1,     1,      1, ...
     3,    5,     9,    17,     33, ...
    13,   31,    79,   211,    583, ...
    79,  265,   937,  3433,  12889, ...
   579, 2621, 12501, 62141, 319461, ...

Crossrefs

Columns k=0..2 give A215915, A058892, A293731.

Rows n=0-1 give A000012.

Sequence in context: A083075 A335333 A341470 * A195892 A195522 A273169

Adjacent sequences: A293793 A293794 A293795 * A293797 A293798 A293799

Keyword

nonn,tabl,look

Author

Seiichi Manyama, Oct 16 2017

Status

approved