A367471 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^3.

1, 6, 54, 630, 8982, 150966, 2918934, 63772470, 1552910742, 41690570166, 1223096629014, 38924237638710, 1335418262833302, 49129420920630966, 1929262811804022294, 80540656071983191350, 3561781875173605408662, 166331104582900651581366

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Cf. A004123, A367470.

Cf. A226515, A367473.

Sequence in context: A069726 A269477 A305602 * A367475 A081132 A158831

Adjacent sequences: A367468 A367469 A367470 * A367472 A367473 A367474

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved