A038003 Odd Catalan numbers: a(n) = A000108(2^n-1).

1, 1, 5, 429, 9694845, 14544636039226909, 94295850558771979787935384946380125, 11311095732253345760960290897769189975961199415637572612957718759342193629

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Comments

The next term has 150 digits. - Harvey P. Dale, Feb 22 2016

Links

• David Wasserman, May 07 2007, Table of n, a(n) for n = 0..9
• H-Y. Lin, Odd Catalan Numbers modulo 2^k, Integers 11 (2011) #A55
• Eric Weisstein's World of Mathematics, Catalan Number

Crossrefs

Cf. A000108, A094389, A119861, A119908, A120274, A120275.

Intersection of A001790 and A098597. - Dimitri Papadopoulos, Oct 28 2016

Programs

Magma

[Binomial(2^(n+1)-2, 2^n-1)/(2^n): n in [0..10]]; // Vincenzo Librandi, Nov 01 2016

Mathematica

Select[CatalanNumber[Range[0,300]],OddQ] (* Harvey P. Dale, Feb 22 2016 *)

PARI

a(n) = binomial(2^(n+1)-2, 2^n-1)/(2^n); \\ Joerg Arndt, Nov 05 2015

Python

from _future_ import division
A038003_list, c, s = [1, 1], 1, 3
for n in range(2,10**5+1):
    c = (c*(4*n-2))//(n+1)
    if n == s:
        A038003_list.append(c)
        s = 2*s+1 # Chai Wah Wu, Feb 12 2015

Formula

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

a(n-1) = C(2^n,2^(n-1))/(2^n - 1)/2. - Benoit Cloitre, Aug 17 2002

a(n) = A000108(2^n-1). - David Wasserman, May 07 2007