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A367471
Expansion of e.g.f. 1 / (3 - 2 * exp(x))^3.
6
1, 6, 54, 630, 8982, 150966, 2918934, 63772470, 1552910742, 41690570166, 1223096629014, 38924237638710, 1335418262833302, 49129420920630966, 1929262811804022294, 80540656071983191350, 3561781875173605408662, 166331104582900651581366
OFFSET
0,2
FORMULA
a(n) = (1/2) * Sum_{k=0..n} 2^k * (k+2)! * Stirling2(n,k).
a(0) = 1; a(n) = 2*Sum_{k=1..n} (2*k/n + 1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 6*a(n-1) - 3*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, 2^k*(k+2)!*stirling(n, k, 2))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 19 2023
STATUS
approved