|
| |
|
|
A091135
|
|
Number of Dyck paths of semilength n+4, having exactly two long ascents (i.e. ascents of length at least two).
|
|
0
| |
|
|
2, 15, 69, 252, 804, 2349, 6455, 16962, 43086, 106587, 258153, 614520, 1441928, 3342489, 7667883, 17432766, 39321810, 88080615, 196083965, 434110740, 956301612, 2097152325, 4580180319, 9965666682, 21609054614, 46707769779
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Also number of ordered trees with n+4 edges, having exactly two branch nodes (i.e. vertices of outdegree at least two).
|
|
|
FORMULA
| a(n)=(n^2+9n+20)/2+2^(n+1)*(n^2+3n-4). G.f.=(2-3z)/[(1-2z)^3*(1-z)^3].
|
|
|
EXAMPLE
| a(0)=2 because the only Dyck paths of semilength 4 that have exactly two long ascents are UUDDUUDD and UUDUUDDD (here U=(1,1) and D=(1,-1)).
|
|
|
CROSSREFS
| Cf. A000108.
Sequence in context: A117393 A055206 A146757 * A056037 A125903 A178321
Adjacent sequences: A091132 A091133 A091134 * A091136 A091137 A091138
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2004
|
| |
|
|
