A006634 From generalized Catalan numbers. (Formerly M4648)

1, 9, 72, 570, 4554, 36855, 302064, 2504304, 20974005, 177232627, 1509395976, 12943656180, 111676661460, 968786892675, 8445123522144, 73940567860896, 649942898236596, 5733561315124260, 50744886833898400, 450461491952952690, 4009721145437152530, 35782256673785401065

Offset

0,2

References

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Plouffe, Simon, Approximations of generating functions and a few conjectures, arXiv:0911.4975 [math.NT], 2002.

Formula

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

G.f.: g^9 where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Apr 22 2013

Maple

series(RootOf(g = 1+x*g^4, g)^9, x=0, 30); # Mark van Hoeij, Apr 22 2013

Mathematica

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 *)

Prog

(PARI)
N = 3*66;  x = 'x + O('x^N);
g=serreverse(x-x^4)/x;
gf=g^9;  v=Vec(gf);
vector(#v\3, n, v[3*n-2])
/* Joerg Arndt, Apr 23 2013 */

Crossrefs

Sequence in context: A084327 A057085 A076765 * A129328 A162960 A163391

Adjacent sequences: A006631 A006632 A006633 * A006635 A006636 A006637

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Joerg Arndt, Apr 23 2013

Status

approved