A305401 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j).

1, 1, 0, 1, 1, 1, 1, 2, 3, 0, 1, 3, 9, 10, 1, 1, 4, 19, 56, 43, 0, 1, 5, 33, 174, 457, 225, 1, 1, 6, 51, 400, 2107, 4626, 1393, 0, 1, 7, 73, 770, 6433, 31779, 55969, 9976, 1, 1, 8, 99, 1320, 15451, 129060, 574129, 788192, 81201, 0, 1, 9, 129, 2086, 31753, 387045, 3103873, 12088488, 12667041, 740785, 1

Offset

0,8

Links

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

Formula

A(n,k) = k*n*A(n-1,k) + A(n-2,k) for n>1.

Example

Square array begins:
   1,  1,   1,    1,    1,     1, ...
   0,  1,   2,    3,    4,     5, ...
   1,  3,   9,   19,   33,    51, ...
   0, 10,  56,  174,  400,   770, ...
   1, 43, 457, 2107, 6433, 15451, ...

Crossrefs

Columns k=0-3 give A059841, A001040(n+1), A036243, A305459.

Rows n=0-2 give A000012, A001477, A058331.

Main diagonal gives A305465.

Cf. A305466.

Sequence in context: A143325 A307910 A128888 * A306100 A294046 A320079

Adjacent sequences: A305398 A305399 A305400 * A305402 A305403 A305404

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 02 2018

Status

approved