A367470 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^2.

1, 4, 28, 268, 3244, 47404, 810988, 15891628, 350851564, 8615761324, 232911898348, 6872755977388, 219799913877484, 7572909749244844, 279630706025296108, 11016315458773541548, 461211305514352065004, 20448268640012928321964

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} 2^k * (k+1)! * Stirling2(n,k).

a(0) = 1; a(n) = 2*Sum_{k=1..n} (k/n + 1) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 4*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+1)!*stirling(n, k, 2));

Crossrefs

Cf. A004123, A367471.

Cf. A005649, A367472.

Cf. A367474.

Sequence in context: A284756 A316144 A138272 * A361049 A245060 A191686

Adjacent sequences: A367467 A367468 A367469 * A367471 A367472 A367473

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved