0,3

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

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

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

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

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.

R. Cori et al., Shuffle of parenthesis systems and Baxter permutations, J. Combin. Theory, A 43 (1986), 1-22.

D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableau de Young, pp. 112-125 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 7.16(b), y_4(n), p. 452.

T. D. Noe, Table of n, a(n) for n=0..200

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

There are 26 standard tableaux of size 5, one of them is of length longer than 4 so a(5) = 25

c := n->binomial(2*n, n)/(n+1); seq(c(floor((n+1)/2))*c(floor(n/2+1)), n=0..16);

(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

Cf. A000108, A001405, A001006, A049401, A007579, A007578.

Bisections are A001246 and A005568.

Sequence in context: A032128 A052829 A001998 this_sequence A148093 A148094 A148095

Adjacent sequences: A005814 A005815 A005816 this_sequence A005818 A005819 A005820

nonn,easy

Simon Plouffe and N. J. A. Sloane (njas(AT)research.att.com).

Description corrected Feb 15 1997.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008

Offset chnaged by N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2008