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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).
3
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
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
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 02 2018
STATUS
approved