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%I #9 Nov 08 2017 02:32:21
%S 0,1,2,6,52,540,6846,104832,1883848,38889360,907247770,23608391840,
%T 678039307452,21305543325248,727095737061526,26781816978470400,
%U 1059020025979194128,44746083421419997440,2011929587198990154162,95918808101232854969856
%N E.g.f.: -cos(x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277477/b277477.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ cos(exp(-1)) * n^(n-1).
%t CoefficientList[Series[-Cos[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t Table[Sum[Binomial[n, k] * Cos[Pi*(n-k)/2] * k^(k-1), {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-cos(x)*lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000169, A277462, A277473, A277475, A277478.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 17 2016
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