OFFSET
0,2
FORMULA
a(n) = 3^n + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (27/8)*A004123(n+1) - (1/2)*(2^n + 3/2 + (9/4)*0^n).
PROG
(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=3, t=2) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 21 2023
STATUS
approved