OFFSET
0,2
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A032033(k) * binomial(n-1,k-1) * a(n-k).
a(n) = Sum_{k=0..n} 3^k * A000262(k) * Stirling2(n,k).
a(n) ~ exp(-7/8 - n + 1/(8*log(4/3)) + sqrt(n/log(4/3))) * n^(n - 1/4) / (2*log(4/3)^(n + 1/4)). - Vaclav Kotesovec, May 23 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(exp(x)-1)/(4-3*exp(x)))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 3^k*k!*stirling(j, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 23 2022
STATUS
approved