OFFSET
0,4
LINKS
Winston de Greef, Table of n, a(n) for n = 0..1935
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (3*k)!/k!^3 * binomial(k,n-3*k).
From Vaclav Kotesovec, Mar 23 2023: (Start)
Recurrence: (n-1)*n^2*a(n) = -(n-1)^2*n*a(n-1) + 27*(n-2)*(n-1)^2*a(n-3) + 18*(n-2)*(3*n^2 - 9*n + 2)*a(n-4) + 3*n*(3*n - 11)*(3*n - 7)*a(n-5).
a(n) ~ sqrt(3) * d^n / (2*Pi*n), where d = 3.278393896770041178744966998018587... is the positive real root of the equation d^4 - 27*d - 27 = 0. (End)
PROG
(PARI) a(n) = sum(k=0, n\3, (3*k)!/k!^3*binomial(k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved