A135759 Least Catalan number divisible by 2^n: a(n) = A000108(2^(n+1)-2).

1, 2, 132, 2674440, 3814986502092304, 24139737743045626825711458546273312, 2861304849265668492891140780463352404986232263244287143198790516197234752

Offset: 0

Author

Paul D. Hanna, Dec 02 2007

Keywords

• nonn

Comments

The next term has 150 digits. - Harvey P. Dale, Jan 09 2017

Crossrefs

Cf. A038003 (odd Catalan numbers).

Programs

Mathematica

Table[Binomial[2^(n + 2) - 4, 2^(n + 1) - 2]/(2^(n + 1) - 1), {n,0,10}] (* G. C. Greubel, Nov 07 2016 *)
Table[SelectFirst[CatalanNumber[Range[300]],Divisible[#,2^n]&],{n,0,7}] (* Harvey P. Dale, Jan 09 2017 *)

PARI

{a(n) = binomial(2^(n+2)-4, 2^(n+1)-2) / (2^(n+1)-1)}
for(n=0,8,print1(a(n),", "))

Formula

a(n) = C(2^(n+2)-4, 2^(n+1)-2) / (2^(n+1)-1).