OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(3*k,n-3*k)/k!.
a(0) = 1; a(n) = (n-1)! * Sum_{k=3..n} k * binomial(3,k-3) * a(n-k)/(n-k)!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(1+x))^3)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=3, i, j*binomial(3, j-3)*v[i-j+1]/(i-j)!)); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 16 2023
STATUS
approved