A051789 - OEIS

%I #22 Jul 10 2023 03:03:11

%S 0,0,1,10,91,861,8646,91806,1021735,11817091,141044410,1727867505,

%T 21634392066,275949833550,3576313319580,46995004939590,

%U 625082396235615,8403885722249655,114069363630025650,1561609590480856455,21543838440848427990,299299110934736706690

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

%H Vincenzo Librandi, <a href="/A051789/b051789.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = binomial(binomial(2*n,n)/(n+1),2). - _Zerinvary Lajos_, May 29 2006

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

%p [seq (binomial(binomial(2*n,n)/(n+1),2), n=0..24)]; # _Zerinvary Lajos_, May 29 2006

%t (#(#-1))/2&/@CatalanNumber[Range[0,20]] (* _Harvey P. Dale_, Aug 08 2014 *)

%o (Magma) [Catalan(n)*(Catalan(n)-1)/2: n in [0..20]] // _Vincenzo Librandi_, Aug 09 2014

%Y Cf. A000108.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Dec 10 1999