A186031 Number of Dyck paths of semilength n with a valley (DU) spanning the midpoint.
0, 1, 1, 5, 10, 42, 107, 429, 1234, 4862, 15032, 58786, 190588, 742900, 2490399, 9694845, 33312770, 129644790, 453999656, 1767263190, 6282014804, 24466267020, 88026769844, 343059613650, 1246635155180, 4861946401452, 17815452662152
Offset: 1
Keywords
Examples
For n=4 the 5 paths are UDUD.UDUD, UUDD.UDUD, UDUD.UUDD, UUDD.UUDD and UUUD.UDDD where dot marks the midpoint.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Maple
C:= n-> binomial (2*n, n)/(n+1): a:= n-> C(n-1) -`if` (irem(n, 2)=1, C((n-1)/2)^2, 0): seq (a(n), n=1..40);