A360861 a(n) = Sum_{k=0..n} binomial(n, ceiling(k/2)) * binomial(n, floor(k/2)).

1, 2, 7, 22, 81, 281, 1058, 3830, 14605, 54127, 208110, 782761, 3027038, 11501478, 44668692, 170974710, 666220005, 2564271875, 10018268150, 38728479647, 151631858378, 588229029258, 2307174835212, 8975958379817, 35258881445606, 137501193282026, 540821096592028

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

Row sums of A360859.

Cf. A001405, A018224.

Sequence in context: A047095 A110137 A097967 * A052879 A007867 A241156

Adjacent sequences: A360858 A360859 A360860 * A360862 A360863 A360864

Keyword

nonn

Author

Peter Luschny, Feb 28 2023

Status

approved