%I A005817 M1212
%S A005817 1,1,2,4,10,25,70,196,588,1764,5544,17424,56628,184041,613470,2044900,
%T A005817 6952660,23639044,81662152,282105616,987369656,3455793796,12228193432,
%U A005817 43268992144,154532114800,551900410000,1986841476000,7152629313600
%N A005817 C([n/2+1/2])*C([n/2+1]) where C(i) = Catalan numbers A000108.
%C A005817 Number of underdiagonal lattice paths in the first quadrant, going from 
               (0,0) to a point on the x-axis and consisting of n+1 steps from {E=(1,
               0), W=(-1,0), N=(0,1), S=(0,-1)}. Example: a(2)=4 because we have 
               EEE, ENS, EEW and EWE [Gouyou-Beauchamps]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 29 2004
%C A005817 Also the number of standard tableaux of d with height less than or equal 
               to 4. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Mar 24 2007
%C A005817 Also, number of walks within N^2 (the first quadrant of Z^2) starting 
               at (0,0), ending on the vertical axis and consisting of n steps taken 
               from {(-1, 1), (0, -1), (0, 1), (1, -1)} - Manuel Kauers (manuel(AT)kauers.de), 
               Nov 18 2008
%C A005817 Also, number of walks within N^3 (the first octant of Z^3) starting at 
               (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, -1, 
               1), (0, 1, 0), (1, 0, -1)} - Manuel Kauers (manuel(AT)kauers.de), 
               Nov 18 2008
%D A005817 F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of 
               tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 
               463-468.
%D A005817 R. Cori et al., Shuffle of parenthesis systems and Baxter permutations, 
               J. Combin. Theory, A 43 (1986), 1-22.
%D A005817 D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableau de Young, pp. 
               112-125 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes 
               Math. 1234, 1986.
%D A005817 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005817 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 7.16(b), y_4(n), p. 452.
%H A005817 T. D. Noe, <a href="b005817.txt">Table of n, a(n) for n=0..200</a>
%H A005817 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted 
               Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</
               a>.
%H A005817 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>.
%e A005817 There are 26 standard tableaux of size 5, one of them is of length longer 
               than 4 so a(5) = 25
%p A005817 c := n->binomial(2*n,n)/(n+1); seq(c(floor((n+1)/2))*c(floor(n/2+1)), 
               n=0..16);
%o A005817 (PARI) c(n)=binomial(2*n, n)/(n+1) for(n=1,40,print1(c(floor((n+1)/2))*c(floor(n/
               2+1))",")); - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
%Y A005817 Cf. A000108, A001405, A001006, A049401, A007579, A007578.
%Y A005817 Bisections are A001246 and A005568.
%Y A005817 Sequence in context: A032128 A052829 A001998 this_sequence A148093 A148094 
               A148095
%Y A005817 Adjacent sequences: A005814 A005815 A005816 this_sequence A005818 A005819 
               A005820
%K A005817 nonn,easy
%O A005817 0,3
%A A005817 Simon Plouffe and N. J. A. Sloane (njas(AT)research.att.com).
%E A005817 Description corrected Feb 15 1997.
%E A005817 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
%E A005817 Offset chnaged by N. J. A. Sloane (njas(AT)research.att.com), Nov 28 
               2008