OFFSET
0,2
FORMULA
a(n) = 4^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (256/81)*A032033(n) - (1/3)*(3^n + (4/3)*2^n + 16/9 + (64/27)*0^n).
PROG
(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=4, t=3) = 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