A051789 a(n) = C(n)*(C(n)-1)/2, where C(n) are the Catalan numbers (A000108).

0, 0, 1, 10, 91, 861, 8646, 91806, 1021735, 11817091, 141044410, 1727867505, 21634392066, 275949833550, 3576313319580, 46995004939590, 625082396235615, 8403885722249655, 114069363630025650, 1561609590480856455, 21543838440848427990, 299299110934736706690

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = binomial(binomial(2*n,n)/(n+1),2). - Zerinvary Lajos, May 29 2006

Sum_{n>=0} a(n)/16^n = 8/Pi + 2*sqrt(3) - 6. - Amiram Eldar, Jul 10 2023

Maple

[seq (binomial(binomial(2*n, n)/(n+1), 2), n=0..24)]; # Zerinvary Lajos, May 29 2006

Mathematica

(#(#-1))/2&/@CatalanNumber[Range[0, 20]] (* Harvey P. Dale, Aug 08 2014 *)

Prog

(Magma) [Catalan(n)*(Catalan(n)-1)/2: n in [0..20]] // Vincenzo Librandi, Aug 09 2014

Crossrefs

Cf. A000108.

Sequence in context: A096261 A015455 A110410 * A343354 A338678 A347260

Adjacent sequences: A051786 A051787 A051788 * A051790 A051791 A051792

Keyword

nonn

Author

N. J. A. Sloane, Dec 10 1999

Status

approved