A006635 From generalized Catalan numbers.

1, 12, 114, 1012, 8775, 75516, 649264, 5593068, 48336171, 419276660, 3650774820, 31907617560, 279871768995, 2463161027292, 21747225841440, 192575673551584, 1710009515037060, 15223466050169520, 135853465827080970, 1215067013768834100

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

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

• Simon Plouffe, Approximations of generating functions and a few conjectures, Master's Thesis, UQAM 1992; arXiv:0911.4975 [math.NT], 2009.

Crossrefs

Cf. A002293, A196678, A006633, A233658, A233666, A006634, A233667.

Programs

Mathematica

terms = 20; g[] = 0; Do[g[x] = 1 + x g[x]^4 + O[x]^terms, terms];
CoefficientList[g[x]^12, x] (* Jean-François Alcover, Oct 07 2018, after Sean A. Irvine *)

Formula

4F3([3,7/2,15/4,13/4],[5,14/3,13/3],256*x/27) - Simon Plouffe, Master's thesis, UQAM 1992

G.f.: g^12 where g is the g.f. of A002293. - Sean A. Irvine, May 25 2017

Extensions

More terms from Sean A. Irvine, May 25 2017