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 A038003 Odd Catalan numbers; more precisely, A000108(2^n-1). 18
 1, 1, 5, 429, 9694845, 14544636039226909, 94295850558771979787935384946380125, 11311095732253345760960290897769189975961199415637572612957718759342193629 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 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 MATHEMATICA Select[CatalanNumber[Range[0, 300]], OddQ] (* Harvey P. Dale, Feb 22 2016 *) PROG (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 (PARI) a(n) = binomial(2^(n+1)-2, 2^n-1)/(2^n); \\ Joerg Arndt, Nov 05 2015 (MAGMA) [Binomial(2^(n+1)-2, 2^n-1)/(2^n): n in [0..10]]; // Vincenzo Librandi, Nov 01 2016 CROSSREFS Cf. A000108, A094389, A119861, A119908, A120274, A120275. Intersection of A001790 and A098597. - Dimitri Papadopoulos, Oct 28 2016 Sequence in context: A147684 A199090 A218393 * A054332 A145247 A317345 Adjacent sequences:  A038000 A038001 A038002 * A038004 A038005 A038006 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 30 10:56 EST 2021. Contains 349419 sequences. (Running on oeis4.)