A063017 - OEIS

%I #17 Jun 26 2018 13:02:58

%S 1,3,20,165,1484,13986,135960,1352637,13707980,141061206,1470489800,

%T 15500280978,164967244792,1770548369700,19143828730800,

%U 208347968093085,2280730450967820,25096531231958670,277445318198433000

%N a(n) = Catalan(n)*(3^(n+1) - 2^(n+1) + 1)/2.

%H Harry J. Smith, <a href="/A063017/b063017.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Catalan(n)*(3^(n+1) - 2^(n+1) + 1)/2;

%F o.g.f: -(sqrt(1-4x) - sqrt(1-8x)+ sqrt(1-12x) -1)/(4x).

%t Table[CatalanNumber[n] (3^(n + 1) - 2^(n + 1) + 1)/2, {n, 0, 20}] (* _Wesley Ivan Hurt_, Jan 30 2014 *)

%o (PARI) a(n)={binomial(2*n, n)/(n + 1)*(3^(n+1) - 2^(n+1) + 1)/2} \\ _Harry J. Smith_, Aug 16 2009

%Y Cf. A000108, A063016.

%K easy,nonn

%O 0,2

%A _Olivier Gérard_, Jul 04 2001

%E Formula corrected by _Harry J. Smith_, Aug 16 2009