A368283 Expansion of e.g.f. exp(2*x) / (1 + log(1 - x)).

1, 3, 11, 52, 320, 2486, 23402, 258252, 3263528, 46433648, 734322672, 12776283136, 242519067056, 4987324250416, 110454579648688, 2621008072506592, 66341399843669760, 1784150447268259456, 50804574646886197888, 1527058892582680257024

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=2^i+sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A007840, A291979, A330149, A368284.

Cf. A368285.

Sequence in context: A054362 A129833 A321585 * A107958 A378159 A253972

Adjacent sequences: A368280 A368281 A368282 * A368284 A368285 A368286

Keyword

nonn

Author

Seiichi Manyama, Dec 19 2023

Status

approved