OFFSET
1,5
FORMULA
T(n, k) = (k/n) * Sum_{j=0..n} (-1)^(j-k) * binomial(n,j) * binomial(j,-n-k+2*j).
T(n, k) = binomial(n, k)*hypergeom([(k - n)/2, (k - n + 1)/2], [k + 2], -4)*(-1)^(n - k), assuming offset = 0. - Peter Luschny, May 19 2021
EXAMPLE
1;
-1, 1;
0, -2, 1;
2, 1, -3, 1;
-3, 4, 3, -4, 1;
-1, -10, 5, 6, -5, 1;
11, 4, -21, 4, 10, -6, 1;
MAPLE
# Assuming offset = 0.
T := (n, k) -> (-1)^(n-k)*binomial(n, k)*hypergeom([(k-n)/2, (k-n+1)/2], [k+2], -4): for n from 0 to 9 do seq(simplify(T(n, k)), k=0..n) od; # Peter Luschny, May 19 2021
PROG
(Maxima)
T(n, k):=(k*sum(binomial(j, -n-k+2*j)*(-1)^(j-k)*binomial(n, j), j, 0, n))/n;
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Vladimir Kruchinin, Dec 17 2011
EXTENSIONS
More terms from Sean A. Irvine, Mar 03 2021
STATUS
approved