A063017 a(n) = Catalan(n)*(3^(n+1) - 2^(n+1) + 1)/2.
1, 3, 20, 165, 1484, 13986, 135960, 1352637, 13707980, 141061206, 1470489800, 15500280978, 164967244792, 1770548369700, 19143828730800, 208347968093085, 2280730450967820, 25096531231958670, 277445318198433000
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..200
Programs
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Mathematica
Table[CatalanNumber[n] (3^(n + 1) - 2^(n + 1) + 1)/2, {n, 0, 20}] (* Wesley Ivan Hurt, Jan 30 2014 *) -
PARI
a(n)={binomial(2*n, n)/(n + 1)*(3^(n+1) - 2^(n+1) + 1)/2} \\ Harry J. Smith, Aug 16 2009
Formula
a(n) = Catalan(n)*(3^(n+1) - 2^(n+1) + 1)/2;
o.g.f: -(sqrt(1-4x) - sqrt(1-8x)+ sqrt(1-12x) -1)/(4x).
Extensions
Formula corrected by Harry J. Smith, Aug 16 2009