0,2

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

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

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

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

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.

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=1..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 A124419 A006901 A123422

Adjacent sequences: A005814 A005815 A005816 this_sequence A005818 A005819 A005820

nonn,easy

Simon Plouffe and njas

Description corrected Feb 15 1997.

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