A277502 - OEIS

%I #8 Nov 13 2017 02:45:09

%S 0,1,2,10,72,724,9184,142080,2587392,54290256,1289277440,34191270752,

%T 1001513996288,32113767783616,1118831623585792,42084750888906240,

%U 1699836383279448064,73377208318764134656,3371248736937012363264,164251735270613613412864

%N E.g.f.: -LambertW(-arcsin(x)).

%H G. C. Greubel, <a href="/A277502/b277502.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) ~ sqrt(tan(exp(-1))) * exp(1/2 - n) * n^(n-1) / sin(exp(-1))^n.

%t CoefficientList[Series[-LambertW[-ArcSin[x]], {x, 0, 20}], x] * Range[0, 20]!

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(-lambertw(-asin(x))))) \\ _G. C. Greubel_, Nov 12 2017

%Y Cf. A277469, A277483, A277503.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 18 2016