A006635 From generalized Catalan numbers. (Formerly M4860)

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

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

Table of n, a(n) for n=0..19.

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

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

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 *)

Crossrefs

Sequence in context: A125400 A331515 A154237 * A062386 A080602 A333299

Adjacent sequences: A006632 A006633 A006634 * A006636 A006637 A006638

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Sean A. Irvine, May 25 2017

Status

approved