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Denominators of partial sums of Catalan numbers scaled by powers of 1/12.
5

%I #18 Jun 13 2022 07:49:45

%S 1,12,72,1728,10368,41472,248832,11943936,214990848,2579890176,

%T 15479341056,371504185344,2229025112064,26748301344768,53496602689536,

%U 1711891286065152,10271347716390912,369768517790072832

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

%C Numerators are given under A120782.

%C 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

%H G. C. Greubel, <a href="/A120783/b120783.txt">Table of n, a(n) for n = 0..925</a>

%F 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).

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

%o (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108

%o a(n) = denominator(sum(k=0, n, C(k)/12^k)); \\ _Michel Marcus_, Mar 02 2016

%Y Cf. A000108, A120782.

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006