OFFSET
0,3
FORMULA
a(n) = (-1)^(n-1)*n^2*hypergeom([1 - n, 1 - n, n + 1], [3/2, 2], -1/4) for n >= 1.
D-finite with recurrence 4*n*(2*n-1)*(9789*n-26254)*a(n) +2*(28924*n^3-27550*n^2-236727*n+284748)*a(n-1) +2*(342172*n^3-1352012*n^2+1027500*n+356439)*a(n-2) -2*(n-3)*(43143*n^2-783097*n+1918735)*a(n-3) -5*(5116*n-30173)*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jul 27 2022
MAPLE
a := n -> add((-1)^(n - k)*binomial(n, k)*binomial(n + k - 1, n-k), k = 0..n):
seq(a(n), n = 0..28);
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+k-1, n-k)); \\ Michel Marcus, Mar 07 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Mar 07 2022
STATUS
approved