A293718 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*x^j).

1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 13, 1, 1, 1, 5, 31, 73, 1, 1, 1, 5, 31, 145, 281, 1, 1, 1, 5, 31, 241, 1181, 1741, 1, 1, 1, 5, 31, 241, 1661, 9661, 8485, 1, 1, 1, 5, 31, 241, 2261, 16861, 77155, 57233, 1, 1, 1, 5, 31, 241, 2261, 20461, 181315, 794081

Offset

0,9

Links

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

Formula

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k,n)} j^2*A(n-j,k)/(n-j)!.

Example

Square array begins:
   1,   1,    1,    1,    1, ...
   1,   1,    1,    1,    1, ...
   1,   5,    5,    5,    5, ...
   1,  13,   31,   31,   31, ...
   1,  73,  145,  241,  241, ...
   1, 281, 1181, 1661, 2261, ...

Crossrefs

Columns k=1..4 give A000012, A115329, A293716, A293717.

Rows n=0-1 give A000012.

Main diagonal gives A082579.

Cf. A293669, A293724.

Sequence in context: A365403 A373439 A035316 * A068316 A359945 A284252

Adjacent sequences: A293715 A293716 A293717 * A293719 A293720 A293721

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 15 2017

Status

approved