A368236 Expansion of e.g.f. 1/(exp(-x) - 2*x).

1, 3, 17, 145, 1649, 23441, 399865, 7957881, 180997857, 4631289697, 131670338921, 4117813225769, 140486274499345, 5192341564319313, 206669931188282073, 8813624820931402201, 400922608851086766017, 19377398675442025382081, 991639882680576890150089

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

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

a(n) ~ n! / (2 * LambertW(1/2)^(n+1) * (LambertW(1/2) + 1)). - Vaclav Kotesovec, Dec 29 2023

Prog

(PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+1)^k/k!);

Crossrefs

Cf. A072597, A368237.

Cf. A336947, A368233.

Sequence in context: A298691 A362282 A051442 * A162650 A015735 A290579

Adjacent sequences: A368233 A368234 A368235 * A368237 A368238 A368239

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2023

Status

approved