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
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..1328
Programs
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Mathematica
Table[Sum[(3*k)!/k!^3 * Binomial[k,n-2*k], {k,0,n/2}], {n,0,20}] (* Vaclav Kotesovec, Mar 23 2023 *) -
PARI
a(n) = sum(k=0, n\2, (3*k)!/k!^3*binomial(k, n-2*k));
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)