OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (1/2)*(binomial(2*n+1,n)+binomial(n,floor(n/2))^2). - Tani Akinari, Jul 12 2023
MATHEMATICA
A360861[n_]:=(Binomial[2n+1, n]+Binomial[n, Floor[n/2]]^2)/2;
Array[A360861, 30, 0] (* Paolo Xausa, Dec 11 2023 *)
PROG
(Python)
from math import comb
def A360861(n): return sum(comb(n, m:=k>>1)**2*(n-m)//(m+1) for k in range(1, n+1, 2)) + sum(comb(n, k>>1)**2 for k in range(0, n+1, 2)) # Chai Wah Wu, Feb 28 2023
(Maxima) a(n):=(1/2)*(binomial(2*n+1, n)+(binomial(n, floor(n/2)))^2); /* Tani Akinari, Jul 12 2023 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 28 2023
STATUS
approved