A120783 Denominators of partial sums of Catalan numbers scaled by powers of 1/12.

1, 12, 72, 1728, 10368, 41472, 248832, 11943936, 214990848, 2579890176, 15479341056, 371504185344, 2229025112064, 26748301344768, 53496602689536, 1711891286065152, 10271347716390912, 369768517790072832

Offset: 0

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• frac
• easy

Comments

Numerators are given under A120782.

It appears that the terms of this sequence are denominators of the power series expansion of 1+sqrt(x) at x=3, scaled by 1/(2*sqrt(3)). - Alexander R. Povolotsky, Mar 01 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 0..925

Crossrefs

Cf. A000108, A120782.

Programs

Mathematica

Denominator@ Table[Sum[CatalanNumber@ k/12^k, {k, 0, n}], {n, 0, 17}] (* Michael De Vlieger, Mar 03 2016 *)

PARI

C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = denominator(sum(k=0, n, C(k)/12^k)); \\ Michel Marcus, Mar 02 2016

Formula

a(n) = denominator(r(n)), with the rationals r(n) = Sum_{k=0..n} C(k)/12^k with C(k) = A000108(k) (Catalan numbers).