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A006634 From generalized Catalan numbers.
(Formerly M4648)
7
1, 9, 72, 570, 4554, 36855, 302064, 2504304, 20974005, 177232627, 1509395976, 12943656180, 111676661460, 968786892675, 8445123522144, 73940567860896, 649942898236596, 5733561315124260, 50744886833898400, 450461491952952690, 4009721145437152530, 35782256673785401065 (list; graph; refs; listen; history; text; internal format)
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, Master Thesis, copy at the arXiv site

FORMULA

G.f.: 4F3([9/4, 5/2, 11/4, 3],[10/3, 11/3, 4],256/27*x), - Simon Plouffe, Master 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-Fran├žois 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, Joerg Arndt, Apr 23 2013

STATUS

approved

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)