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).

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, 720, 1, 1, 33, 211, 841, 2261, 4051, 5040, 1, 1, 65, 583, 3049, 10821, 24781, 37633, 40320, 1, 1, 129, 1651, 11353, 54221, 162601, 309835, 394353, 362880, 1, 1, 257

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*A(n-j,k)/(n-j)! for n > 0.

Example

Square array begins:
     1,   1,    1,     1,     1, ...
     1,   1,    1,     1,     1, ...
     2,   3,    5,     9,    17, ...
     6,  13,   31,    79,   211, ...
    24,  73,  241,   841,  3049, ...
   120, 501, 2261, 10821, 54221, ...

Crossrefs

Columns k=0..4 give A000142, A000262, A082579, A255807, A255819.

Rows n=0-1 give A000012.

Main diagonal gives A293786.

Sequence in context: A156540 A156582 A156953 * A156881 A376554 A056646

Adjacent sequences: A293782 A293783 A293784 * A293786 A293787 A293788

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 16 2017

Status

approved