OFFSET
1,2
COMMENTS
A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down) and L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps.
LINKS
E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203
FORMULA
a(n) = Sum_{k=1..n} k*A129161(n,k).
EXAMPLE
a(2)=5 because the paths UDUD, UUDD and UUDL have heights 1, 2 and 2, respectively.
MAPLE
H[0]:=1: for k from 1 to 32 do H[k]:=simplify((1+z*H[k-1]-z)/(1-z*H[k-1])) od: for k from 1 to 32 do h[k]:=factor(simplify(H[k]-H[k-1])) od: for k from 1 to 32 do hser[k]:=series(h[k], z=0, 30) od: T:=(n, k)->coeff(hser[k], z, n): seq(add(k*T(n, k), k=1..n), n=1..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 03 2007
STATUS
approved