A227466 - OEIS

%I #11 Aug 16 2018 03:00:19

%S 1,2,11,96,1149,17520,324855,7096320,178495065,5081045760,

%T 161485639875,5668185600000,217773547039125,9090267234048000,

%U 409648199646660975,19822083757572096000,1025047834112461784625,56415976360602034176000,3292602426688307236378875

%N E.g.f. equals the series reversion of tanh(x) / exp(x).

%C Note that arctanh(x) = log((1+x)/(1-x))/2.

%F E.g.f. A(x) satisfies: A(x) = arctanh(x*exp(A(x))).

%F a(n) ~ ((1+sqrt(5))/2)^(5*n/2) * n^(n-1)  / (5^(1/4) * exp(n)). - _Vaclav Kotesovec_, Jan 10 2014

%e E.g.f.: A(x) = x + 2*x^2/2! + 11*x^3/3! + 96*x^4/4! + 1149*x^5/5! + 17520*x^6/6! + ...

%e where A( tanh(x)/exp(x) ) = x.

%t Rest[CoefficientList[InverseSeries[Series[Tanh[x]/E^x,{x,0,20}],x],x] * Range[0,20]!] (* _Vaclav Kotesovec_, Jan 10 2014 *)

%o (PARI) {a(n)=local(X=x+x*O(x^n));n!*polcoeff(serreverse(tanh(X)/exp(X)), n)}

%o for(n=1,25,print1(a(n),", "))

%o (PARI) {a(n)=local(A=x); for(i=1,n,A=atanh(x*exp(A+x*O(x^n)))); n!*polcoeff(A, n)}

%o for(n=1,25,print1(a(n),", "))

%Y Cf. A227465.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 14 2013