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 A238085 Expansion of e.g.f.: -LambertW(-sinh(x)). 5

%I

%S 0,1,2,10,72,716,9088,140344,2554240,53540368,1270296064,33653698464,

%T 984753299456,31542901202112,1097763264864256,41247391653500800,

%U 1664188908529156096,71759140177774010624,3293251384307726942208,160272893566770148403712

%N Expansion of e.g.f.: -LambertW(-sinh(x)).

%H Vincenzo Librandi, <a href="/A238085/b238085.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) ~ (exp(-2)+1)^(1/4) * n^(n-1) / ((log(sqrt(1+exp(-2)) + exp(-1)) )^(n-1/2) * exp(n-1/2)).

%p a:=series( -LambertW(-sinh(x)),x=0,20): seq(n!*coeff(a,x,n),n=0..19); # _Paolo P. Lava_, Mar 27 2019

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

%o (PARI) x='x+('x^30); concat([0], Vec(serlaplace(-lambertw(-sinh(x))))) \\ _G. C. Greubel_, Feb 19 2018

%Y Cf. A219503, A214654, A274279, A277463, A277476.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Feb 17 2014

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)