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%I #9 Nov 10 2017 07:37:19
%S 0,0,2,6,40,340,3984,57050,982528,19616328,446355840,11384327438,
%T 321701896704,9973046260060,336499112011776,12274383608508450,
%U 481282311712489472,20185816487436968208,901732370496365076480,42742176871086712813974,2142556308913381810012160
%N E.g.f.: -arcsin(x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277483/b277483.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ arcsin(exp(-1)) * n^(n-1).
%t CoefficientList[Series[-ArcSin[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t Flatten[{0, Table[Sum[Binomial[n, k] * (1-(-1)^k)/2 * (k-2)!!^2 * (n-k)^(n-k-1), {k, 1, n-1}], {n, 1, 20}]}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^50); concat([0,0], Vec(serlaplace(- asin(x)*lambertw(-x) ))) \\ _G. C. Greubel_, Nov 08 2017
%Y Cf. A000169, A277469, A277473, A277484.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 17 2016
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