OFFSET
0,3
COMMENTS
Related to the Motzkin triangle A064189 counting certain lattice paths.
FORMULA
MAPLE
alias(C=binomial):
a := n -> add(C(n, j)*(C(n - j, j + n/2 - 1/4 + (-1)^n/4) - C(n - j, j + n/2 + 7/4 + (-1)^n/4)), j = 0..n): seq(a(n), n = 0..32);
MATHEMATICA
a[n_] := Binomial[n, n/2 - 1/4 + (-1)^n/4] Hypergeometric2F1[-n/4 - 1/8 + (-1)^n/8, -n/4 + 3/8 + (-1)^n/8, n/2 + 7/4 + (-1)^n/4, 4];
Table[a[n], {n, 0, 32}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, May 19 2021
STATUS
approved