OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-k,n-3*k)/(6^k * k!).
From Vaclav Kotesovec, Jun 18 2024: (Start)
Recurrence: 6*a(n) = 6*(3*n-2)*a(n-1) - 6*(n-1)*(3*n-4)*a(n-2) + 3*(n-2)*(n-1)*(2*n-3)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4).
a(n) ~ 3^(-1/3) * exp(19/72 - 3^(-2/3)*n^(1/3) + 3^(2/3)*n^(2/3)/2 - n) * n^(n + 1/6). (End)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, binomial(n-k, n-3*k)/(6^k*k!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 18 2024
STATUS
approved