A305466 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)^j.

1, 1, 0, 1, 1, -1, 1, 2, 1, 0, 1, 3, 7, 2, 1, 1, 4, 17, 40, 7, 0, 1, 5, 31, 150, 313, 33, -1, 1, 6, 49, 368, 1783, 3090, 191, 0, 1, 7, 71, 730, 5857, 26595, 36767, 1304, 1, 1, 8, 97, 1272, 14551, 116772, 476927, 511648, 10241, 0, 1, 9, 127, 2030, 30457, 363045, 2796671, 9988872, 8149601, 90865, -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,  1,   7,   17,   31,    49, ...
    0,  2,  40,  150,  368,   730, ...
    1,  7, 313, 1783, 5857, 14551, ...

Crossrefs

Columns k=0-3 give A056594, A058797, A093985(n-1), A305471.

Rows n=0-2 give A000012, A001477, A056220.

Main diagonal gives A305467.

Cf. A305401.

Sequence in context: A320080 A246106 A322836 * A160114 A213028 A287698

Adjacent sequences: A305463 A305464 A305465 * A305467 A305468 A305469

Keyword

sign,tabl

Author

Seiichi Manyama, Jun 02 2018

Status

approved