

A000782


a(n) = 2*Catalan(n)Catalan(n1).


5



1, 3, 8, 23, 70, 222, 726, 2431, 8294, 28730, 100776, 357238, 1277788, 4605980, 16715250, 61020495, 223931910, 825632610, 3056887680, 11360977650, 42368413620, 158498860260, 594636663660, 2236748680998, 8433988655580, 31872759742852, 120699748759856
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OFFSET

1,2


COMMENTS

a(n) = (7n5)/(n+1) * C(n1), where C(n) = A000108(n).  Ralf Stephan, Jan 13 2004
Number of Dyck (n+1)paths that have a leading or trailing hill.  David Scambler, Aug 22 2012


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
GuoNiu Han, Enumeration of Standard Puzzles
GuoNiu Han, Enumeration of Standard Puzzles [Cached copy]
J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 12851332.


FORMULA

Expansion of (1+x^1*C^1)*C^2, where C = (1(14*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
Also, apart from initial term, expansion of (1+x^2*C^2)*C, where C = (1(14*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
a(n) = leftmost column term of M^(n1)*V, where M = a tridiagonal matrix with 1's in the super and subdiagonals, (1,2,2,2,...) in the main diagonal; and the rest zeros. V = the vector [1,2,0,0,0,...].  Gary W. Adamson, Jun 16 2011
a(n) = A000108(n+1)  A026012(n1).  David Scambler, Aug 22 2012


MATHEMATICA

CoefficientList[Series[(1+x*(1(14*x)^(1/2))/(2*x)^1)*((1(14*x)^(1/2))/(2*x))^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 10 2012 *)


PROG

(MAGMA) [2*Catalan(n)Catalan(n1): n in [1..30]]; // Vincenzo Librandi, Jun 10 2012


CROSSREFS

Partial sums of A071735. Cf. A000108.
Essentially the same as A061557.
Sequence in context: A184120 A215512 A061557 * A148775 A148776 A127385
Adjacent sequences: A000779 A000780 A000781 * A000783 A000784 A000785


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


STATUS

approved



