%I #11 Nov 08 2017 02:31:14
%S 1,1,3,24,233,2860,42875,758856,15488657,358164432,9254769459,
%T 264273873600,8264362186489,280896392748608,10310601442639147,
%U 406479520869636480,17129450693008029729,768404013933189112064,36557893891263190204259,1838650651518153170939904
%N E.g.f.: cos(x)/(1 + LambertW(-x)).
%H G. C. Greubel, <a href="/A277462/b277462.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ cos(exp(-1)) * n^n.
%t CoefficientList[Series[Cos[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%t Table[Cos[Pi*n/2] + Sum[Binomial[n, k] * Cos[Pi*(n-k)/2] * k^k, {k, 1, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace(cos(x)/(1 + lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000312, A086331, A277461, A277464.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 16 2016