%I A006335 M2094
%S A006335 1,2,16,192,2816,46592,835584,15876096,315031552,6466437120,136383037440,
               2941129850880,
%T A006335 64614360416256,1442028424527872,32619677465182208,746569714888605696,
               17262927525017812992,
%U A006335 402801642250415636480,9474719710174783733760,224477974671833337692160
%N A006335 4^n*(3*n)!/((n+1)!*(2*n+1)!).
%C A006335 Number of planar lattice walks of length 3n starting and ending at (0,
               0), remaining in the first quadrant and using only NE,W,S steps.
%D A006335 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006335 G. Kreweras, Sur une classe de problemes de denombrement lies au treillis 
               des partitions des entiers, Cahiers du Bureau Universitaire de Recherche 
               Op\'{e}rationnelle, Institut de Statistique, Universit\'{e} de Paris, 
               6 (1965), circa p. 82.
%H A006335 M. Bousquet-M\'elou, <a href="http://arXiv.org/abs/math.CO/0401067">Walks 
               in the quarter plane: Kreweras' algebraic model</a>
%H A006335 M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter 
               plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</
               a>.
%F A006335 G.f.: (1/(12*x)) * (hypergeom([ -2/3, -1/3],[1/2],27*x)-1) [From Mark 
               van Hoeij (hoeij(AT)math.fsu.edu), Nov 02 2009]
%t A006335 aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, 
               j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = 
               aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, 1 + 
               j, -1 + n]]; Table[aux[0, 0, 3 n], {n, 0, 25}] - Manuel Kauers (manuel(AT)kauers.de), 
               Nov 18 2008
%o A006335 (PARI) a(n)=if(n<0,0,4^n*(3*n)!/(n+1)!/(2*n+1)!)
%Y A006335 Equals 2^(n-1) * A000309(n-1) for n>1.
%Y A006335 Cf. A098272. First row of array A098273.
%Y A006335 Sequence in context: A011553 A123898 A118644 this_sequence A051711 A012683 
               A012677
%Y A006335 Adjacent sequences: A006332 A006333 A006334 this_sequence A006336 A006337 
               A006338
%K A006335 nonn,easy
%O A006335 1,2
%A A006335 N. J. A. Sloane (njas(AT)research.att.com).
%E A006335 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 20 2008 at 
               the suggestion of R. J. Mathar