%I #11 Jun 12 2017 00:03:32

%S 0,1,2,11,104,1241,18216,317715,6414848,147107953,3776164000,

%T 107253230171,3339157316736,113070818225353,4137170839854976,

%U 162653198951193059,6837934005096620032,306093463368534049761,14535589272368159900160,729835620496621069643179

%N E.g.f.: sin(x)/(1+LambertW(-x)).

%H G. C. Greubel, <a href="/A277461/b277461.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) ~ sin(exp(-1)) * n^n.

%t CoefficientList[Series[Sin[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!

%t Table[Sin[Pi*n/2] + Sum[Binomial[n, k] * Sin[Pi*(n-k)/2] * k^k, {k, 1, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Oct 28 2016 *)

%o (PARI) x = 'x + O('x^30); concat(0, Vec(serlaplace(sin(x)/(1+lambertw(-x))))) \\ _Michel Marcus_, Jun 12 2017

%Y Cf. A000312, A086331, A277462, A277463.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 16 2016