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%I #44 Mar 21 2022 06:25:17
%S 1,1,2,6,20,70,256,969,3762,14894,59904,244088,1005452,4180096,
%T 17516936,73913705,313774854,1339162028,5742691704,24731501410,
%U 106919054880,463844340060,2018673093000,8810852089650,38558866555248
%N Revert transform of 1 - x - x^3.
%C Series reversion of x-x^2-x^4. - _Joerg Arndt_, May 24 2011
%H Vincenzo Librandi, <a href="/A049140/b049140.txt">Table of n, a(n) for n = 1..100</a>, format errors corrected by _Vaclav Kotesovec_, Aug 07 2013
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=659">Encyclopedia of Combinatorial Structures 659</a>
%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.
%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = sum(j=0..(n-1)/2, binomial(n-2*j-1,j)*binomial(2*n-2*j-2,n-1))/n. - _Vladimir Kruchinin_, May 24 2011
%F D-finite with recurrence 31*n*(n-1)*(n-2)*(140*n-383)*a(n) -8*(n-1)*(n-2)*(2800*n^2 -11860*n+11583)*a(n-1) +4*(n-2)*(4480*n^3-30176*n^2+66916*n-48753)*a(n-2) -8*(4*n-11)*(4*n-13)*(140*n-243)*(2*n-5)*a(n-3) = 0. - _R. J. Mathar_, Sep 29 2012
%t CoefficientList[1/x InverseSeries[x*(1-x-x^3) + O[x]^26], x] (* _Jean-François Alcover_, Jul 20 2018 *)
%o (Maxima)
%o a(n):=sum(binomial(n-2*j-1,j)*binomial(2*n-2*j-2,n-1),j,0,(n-1)/2)/n; /* _Vladimir Kruchinin_, May 24 2011 */
%o (PARI) Vec(serreverse(x*(1-x-x^3+O(x^66)))) /* _Joerg Arndt_, May 24 2011 */
%K nonn
%O 1,3
%A _Olivier Gérard_
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