|
Search: id:A071718
|
|
|
| A071718 |
|
Expansion of (1+x^2*C)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. |
|
+0
1
|
|
| 1, 3, 10, 32, 104, 345, 1166, 4004, 13936, 49062, 174420, 625328, 2258416, 8209045, 30008790, 110255100, 406923360, 1507973610, 5608843020, 20931740640, 78354322800, 294127079610, 1106939020044, 4175827174152, 15787544777504
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n)=number of Dyck (n+3)-paths whose third from last upstep initiates a long ascent, n>=1. A long ascent is one consisting of 2 or more upsteps. For example, a(1)=3 counts UDuUUDDD, UDuUDUDD, UDuUDDUD (third from last upstep in small type). - David Callan (callan(AT)stat.wisc.edu), Dec 08 2004
|
|
CROSSREFS
|
Sequence in context: A077826 A033505 A063782 this_sequence A134952 A149028 A126183
Adjacent sequences: A071715 A071716 A071717 this_sequence A071719 A071720 A071721
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2002
|
|
|
Search completed in 0.002 seconds
|
