A259885 a(n) = max{T(n,k), k=1..n}, where T(n,k) is the number of Dyck paths of length 2n and height k (1<=k<=n).

1, 1, 3, 7, 18, 57, 169, 484, 1684, 5661, 18579, 59917, 214058, 760487, 2665884, 9246276, 31945379, 117939506, 431530926, 1567159901, 5655480303, 20299352107, 74300429926, 278279597781, 1037075511926, 3848154018734, 14224439297732, 52402156308977

Offset: 1

Author

Gheorghe Coserea, Jul 07 2015

Keywords

• nonn
• walk

Examples

			For n=4, a(4)=7 because T(4,1)=1, T(4,2)=7, T(4,3)=5, T(4,4)=1.
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..1535

Crossrefs

Cf. A080936, A259899 (position of maximum), A265180.

Formula

a(n) ~ 4*K/sqrt(Pi) * 4^n/n^2, where K = 0.2675... (see A265180). - Gheorghe Coserea, Dec 05 2015