login
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.
4
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
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
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jun 02 2018
STATUS
approved