A129162 Sum of heights of all skew Dyck paths of semilength n.
1, 5, 23, 103, 462, 2086, 9493, 43521, 200855, 932429, 4350995, 20395349, 95987113, 453354623, 2148027772, 10206485598, 48621125308, 232156538970, 1110842790406, 5325499426116, 25576096186920, 123030491611330
Offset: 1
Keywords
Examples
a(2)=5 because the paths UDUD, UUDD and UUDL have heights 1, 2 and 2, respectively.
Links
- E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203
Crossrefs
Cf. A129161.
Programs
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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);
Formula
a(n) = Sum_{k=1..n} k*A129161(n,k).
Comments