OFFSET
1,3
COMMENTS
Series reversion of x-x^2-x^4. - Joerg Arndt, May 24 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100, format errors corrected by Vaclav Kotesovec, Aug 07 2013
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 659
Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.
Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
FORMULA
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
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
MATHEMATICA
CoefficientList[1/x InverseSeries[x*(1-x-x^3) + O[x]^26], x] (* Jean-François Alcover, Jul 20 2018 *)
PROG
(Maxima)
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 */
(PARI) Vec(serreverse(x*(1-x-x^3+O(x^66)))) /* Joerg Arndt, May 24 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved