login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A366459
Expansion of e.g.f. -log(1 - x^2 * exp(x)).
2
0, 0, 2, 6, 24, 140, 990, 8442, 84056, 955656, 12227130, 173812430, 2717859012, 46362339036, 856770362630, 17050946225250, 363576478312560, 8269357341437072, 199837364514425586, 5113346326011170838, 138106722548779770620, 3926456810081828991780
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=1..floor(n/2)} k^(n-2*k-1)/(n-2*k)!.
a(n) ~ (n-1)! / (2^n *LambertW(1/2)^n). - Vaclav Kotesovec, Dec 29 2023
PROG
(PARI) a(n) = n!*sum(k=1, n\2, k^(n-2*k-1)/(n-2*k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 14 2023
STATUS
approved