A361738 Diagonal of rational function 1/(1 - (x^2 + y^2 + z^2 + x^3*y*z)).

1, 0, 6, 6, 90, 180, 1770, 5040, 39690, 140280, 964656, 3922380, 24755346, 110486376, 660153780, 3137330196, 18103340970, 89794566576, 506892467796, 2589310074780, 14419819659960, 75181803891480, 415298937771900, 2196704341517400, 12078576672927570

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..1328

Formula

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

From Vaclav Kotesovec, Mar 23 2023: (Start)

Recurrence: (n-1)*n^2*a(n) = -(n-1)^2*n*a(n-1) + 3*(n-1)*(3*n - 4)*(3*n - 2)*a(n-2) + 18*(n-2)*(3*n^2 - 6*n + 1)*a(n-3) + 27*(n-3)*(n-2)*n*a(n-4).

a(n) ~ sqrt(3) * (6*cos(Pi/9))^n / (2*Pi*n). (End)

Mathematica

Table[Sum[(3*k)!/k!^3 * Binomial[k, n-2*k], {k, 0, n/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 23 2023 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (3*k)!/k!^3*binomial(k, n-2*k));

Crossrefs

Cf. A361737, A361739.

Cf. A361729.

Sequence in context: A065239 A146892 A347916 * A320824 A085804 A012125

Adjacent sequences: A361735 A361736 A361737 * A361739 A361740 A361741

Keyword

nonn

Author

Seiichi Manyama, Mar 22 2023

Status

approved