A277469 - OEIS

%I #11 Nov 08 2017 02:31:49

%S 0,1,2,13,112,1329,19344,336533,6778752,155247777,3980956800,

%T 112984562813,3515475849216,118984054897681,4351800687259648,

%U 171034439586509445,7188243684485414912,321696219477456836929,15273278824827215388672,766732102664665113137517

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

%H G. C. Greubel, <a href="/A277469/b277469.txt">Table of n, a(n) for n = 0..385</a>

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

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

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

%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(asin(x)/(1 + lambertw(-x))))) \\ _G. C. Greubel_, Nov 07 2017

%Y Cf. A000312, A086331, A277470.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 16 2016