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A197271 a(n) = 10/((3*n+1)*(3*n+2))*binomial(4*n,n). 3
5, 2, 5, 20, 100, 570, 3542, 23400, 161820, 1159400, 8544965, 64448228, 495508780, 3872033900, 30680401500, 246041115600, 1993987498284, 16310419381080, 134519771966180, 1117653277802000, 9347742311507600, 78652006531467930, 665393840873409150, 5657273782416664200, 48318619683648190500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A combinatorial interpretation for this sequence in terms of a family of plane trees is given in [Schaeffer, Corollary 2 with k = 4].

LINKS

Table of n, a(n) for n=0..24.

G. Schaeffer, A combinatorial interpretation of super-Catalan numbers of order two, (2001).

FORMULA

a(n) = 10/((3*n+1)*(3*n+2))*binomial(4*n,n).

a(n) = A000260(n) * 5*(n+1)/(4*n+1). - Noam Zeilberger, May 20 2019

MATHEMATICA

Table[10/((3n+1)(3n+2)) Binomial[4n, n], {n, 0, 30}] (* Harvey P. Dale, Jan 27 2015 *)

CROSSREFS

Cf. A000139, A000260, A197272.

Sequence in context: A071546 A154649 A100040 * A248260 A253382 A253384

Adjacent sequences:  A197268 A197269 A197270 * A197272 A197273 A197274

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Oct 12 2011

STATUS

approved

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Last modified May 6 13:04 EDT 2021. Contains 343585 sequences. (Running on oeis4.)