OFFSET
0,2
FORMULA
a(n) = 2^n * Sum_{k=0..n} A371400(n, k) * (-1/2)^k.
a(n) = 2^n * binomial(2*n, n) * hypergeom([-n, 1 + n], [-2*n], -1/2).
MAPLE
seq((2^n*add(binomial(k+n, k)*binomial(2*n-k, n)*(-1/2)^k, k=0..n)), n=0..23);
MATHEMATICA
a[n_] := 2^n Binomial[2 n, n] Hypergeometric2F1[-n, 1 + n, -2 n, -1/2];
Table[a[n], {n, 0, 23}]
PROG
(Python)
from math import comb
def A371399(n): return sum(comb(k+n, k)*comb((n<<1)-k, n)*(-1 if k&1 else 1)<<n-k for k in range(n+1)) # Chai Wah Wu, Mar 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Mar 21 2024
STATUS
approved