A368267 Expansion of e.g.f. exp(2*x) / (1 - 2*x*exp(x)).

1, 4, 24, 206, 2344, 33322, 568420, 11312366, 257293872, 6583516946, 187173328444, 5853594770806, 199705444781512, 7381068971010074, 293787494031046740, 12528831526596461438, 569923490454177217120, 27545552296682691393058

Offset

0,2

Links

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

Formula

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

a(n) ~ n! / (4 * LambertW(1/2)^(n+2) * (LambertW(1/2) + 1)). - Vaclav Kotesovec, Dec 29 2023

Prog

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

Crossrefs

Cf. A351762, A368236, A368268, A368269.

Sequence in context: A240297 A050388 A241980 * A297218 A010039 A245407

Adjacent sequences: A368264 A368265 A368266 * A368268 A368269 A368270

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 19 2023

Status

approved