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%I M4648 #37 Dec 15 2019 08:37:38
%S 1,9,72,570,4554,36855,302064,2504304,20974005,177232627,1509395976,
%T 12943656180,111676661460,968786892675,8445123522144,73940567860896,
%U 649942898236596,5733561315124260,50744886833898400,450461491952952690,4009721145437152530,35782256673785401065
%N From generalized Catalan numbers.
%D H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A006634/b006634.txt">Table of n, a(n) for n = 0..200</a>
%H Plouffe, Simon, <a href="http://arxiv.org/abs/0911.4975">Approximations of generating functions and a few conjectures</a>, arXiv:0911.4975 [math.NT], 2002.
%F G.f.: 4F3([9/4, 5/2, 11/4, 3],[10/3, 11/3, 4],256/27*x). - _Simon Plouffe_, Master's Thesis, UQAM, 1992
%F G.f.: g^9 where g = 1+x*g^4 is the g.f. of A002293. - _Mark van Hoeij_, Apr 22 2013
%p series(RootOf(g = 1+x*g^4,g)^9, x=0, 30); # _Mark van Hoeij_, Apr 22 2013
%t f[x_] := HypergeometricPFQ[ {9/4, 5/2, 11/4, 3}, {10/3, 11/3, 4}, 256/27*x]; Series[f[x], {x, 0, 16}] // CoefficientList[#, x]& (* _Jean-François Alcover_, Apr 23 2013, after _Simon Plouffe_ *)
%o (PARI)
%o N = 3*66; x = 'x + O('x^N);
%o g=serreverse(x-x^4)/x;
%o gf=g^9; v=Vec(gf);
%o vector(#v\3,n,v[3*n-2])
%o /* _Joerg Arndt_, Apr 23 2013 */
%K nonn
%O 0,2
%A _Simon Plouffe_
%E More terms from _Joerg Arndt_, Apr 23 2013
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