A361752 a(n) = Sum_{k=0..floor(n/2)} binomial(2*(n-2*k),k) * binomial(2*(n-2*k),n-2*k).

1, 2, 6, 24, 94, 374, 1520, 6252, 25942, 108408, 455586, 1923444, 8151856, 34661252, 147788484, 631660788, 2705471254, 11609393084, 49899207640, 214792704256, 925811868178, 3995288307392, 17260287754284, 74641620619072, 323080683587056, 1399606566298916

Offset

0,2

Comments

Diagonal of rational function 1/(1 - (1 + (x*y)^2) * (x + y)).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/sqrt(1 - 4*x*(1 + x^2)^2).

n*a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-3)*a(n-3) + 2*(2*n-5)*a(n-5) for n > 4.

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(2*(n-2*k), k)*binomial(2*(n-2*k), n-2*k));
(Python)
from math import comb
def A361752(n): return sum(comb(m:=(r:=n-(k<<1))<<1, k)*comb(m, r) for k in range((n>>1)+1)) # Chai Wah Wu, Mar 23 2023

Crossrefs

Cf. A137635, A361753.

Cf. A360266.

Sequence in context: A367274 A375276 A374598 * A115220 A293185 A292984

Adjacent sequences: A361749 A361750 A361751 * A361753 A361754 A361755

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2023

Status

approved