A006635 - OEIS

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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

(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

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

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

Sequence in context: A378504 A331515 A154237 * A062386 A080602 A333299

Adjacent sequences: A006632 A006633 A006634 * A006636 A006637 A006638

KEYWORD

nonn,changed

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from Sean A. Irvine, May 25 2017

STATUS

approved