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A367473
Expansion of e.g.f. 1 / (4 - 3 * exp(x))^3.
4
1, 9, 117, 1953, 39645, 946089, 25926597, 801869553, 27618402285, 1048096422009, 43444114011477, 1952712851250753, 94592798546953725, 4912513525545837129, 272265236648295312357, 16039329591716508497553, 1000809252891040145821965
OFFSET
0,2
FORMULA
a(n) = (1/2) * Sum_{k=0..n} 3^k * (k+2)! * Stirling2(n,k).
a(0) = 1; a(n) = 3*Sum_{k=1..n} (2*k/n + 1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 9*a(n-1) - 4*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, 3^k*(k+2)!*stirling(n, k, 2))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 19 2023
STATUS
approved