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%I #22 Apr 07 2019 19:04:56
%S 1,1,2,4,-6,-232,-3116,-34652,-331680,-2206128,9303480,812562672,
%T 22705836048,484588970448,8345456974368,94936573618176,
%U -635010052507872,-88746666011316480,-3781485264943422528
%N E.g.f. A(x) = Sum_{n>=1} a(n)*x^n/n! is inverse function to exp(x) - x^2 - 1.
%H Vladimir Kruchinin, <a href="http://arxiv.org/abs/1211.3244">The method for obtaining expressions for coefficients of reverse generating functions</a>, arXiv:1211.3244 [math.CO], 2012.
%F a(n) = ((n-1)!*sum(k=1..n-1, binomial(n+k-1,n-1)*sum(j=1..k, (-1)^(j)*binomial(k,j)*sum(l=0..min(j,floor((n+j-1)/2)), (binomial(j,l)*(j-l)!*(-1)^l*Stirling2(n-2*l+j-1,j-l))/(n-2*l+j-1)!)))), n>1, a(1)=1.
%F Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1/abs((1+LambertW(-1/2))^2) = 1.57356815308645229... - _Vaclav Kotesovec_, Jan 23 2014
%t Rest[CoefficientList[InverseSeries[Series[E^x-x^2-1, {x, 0, 20}], x],x]*Range[0, 20]!] (* _Vaclav Kotesovec_, Jan 23 2014 *)
%o (Maxima) a(n):=if n=1 then 1 else ((n-1)!*sum(binomial(n+k-1,n-1)*sum((-1)^(j)*binomial(k,j)*sum((binomial(j,l)*(j-l)!*(-1)^l*stirling2(n-2*l+j-1,j-l))/(n-2*l+j-1)!,l,0,min(j,floor((n+j-1)/2))),j,1,k),k,1,n-1));
%Y Cf. A206304.
%K sign
%O 1,3
%A _Vladimir Kruchinin_, Jan 23 2012
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