A361753 a(n) = Sum_{k=0..floor(n/3)} binomial(2*(n-3*k),k) * binomial(2*(n-3*k),n-3*k).

1, 2, 6, 20, 74, 276, 1044, 3994, 15426, 60008, 234764, 922716, 3640700, 14411952, 57210750, 227659704, 907853778, 3627085932, 14515139376, 58174092472, 233463067284, 938061587212, 3773298437204, 15193083455580, 61230698571372, 246978403761112

Offset

0,2

Comments

Diagonal of rational function 1/(1 - (1 + (x*y)^3) * (x + y)).

Links

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

Formula

G.f.: 1/sqrt(1 - 4*x*(1 + x^3)^2).

Recurrence: n*a(n) = 2*(2*n-1)*a(n-1) + 8*(n-2)*a(n-4) + 2*(2*n-7)*a(n-7). - Vaclav Kotesovec, Mar 23 2023

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*(n-3*k), k)*binomial(2*(n-3*k), n-3*k));
(Python)
from math import comb
def A361753(n): return sum(comb(m:=(r:=n-3*k)<<1, k)*comb(m, r) for k in range(n//3+1)) # Chai Wah Wu, Mar 23 2023

Crossrefs

Cf. A137635, A361752.

Cf. A360267.

Sequence in context: A150150 A150151 A374599 * A376811 A150152 A107284

Adjacent sequences: A361750 A361751 A361752 * A361754 A361755 A361756

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2023

Status

approved