|
Search: id:A091600
|
|
|
| A091600 |
|
Expansion of solution to xA(x)(A(x)-x+1)=A(xA(x)). |
|
+0
1
|
|
| 0, 1, 1, 1, 2, 4, 9, 21, 50, 122, 303, 764, 1950, 5028, 13077, 34265, 90368, 239696, 639011, 1711281, 4601504, 12418610, 33627437, 91334429, 248761858, 679271970, 1859207099, 5099872111, 14017476257, 38600963255, 106485177331
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Series reversion of g.f. A(x) is -A(-x).
For n>=1, a(n) = number of Dyck (n-1)-paths with no matching UU-DD pairs and no DDDDs. Also, a(n) = number of noncrossing partitions of [n-1] in which no block contains two consecutive integers and all blocks have size <=3. For example, a(5)=4 counts 14-2-3, 1-24-3, 1-2-3-4, 13-2-4, where dashes separate the blocks. - David Callan (callan(AT)stat.wisc.edu), Jul 27 2007
|
|
FORMULA
|
G.f. A(x) satisfies A(x)= x +(A(x*A(x))-x*A(x))/(x*A(x)).
|
|
PROGRAM
|
(PARI) a(n)=local(A=x+x^2+O(x^3)); for(i=3, n, A=x+subst((A-x)/x, x, x*A)); polcoeff(A, n)
|
|
CROSSREFS
|
Sequence in context: A027826 A091964 A092423 this_sequence A048285 A051529 A005207
Adjacent sequences: A091597 A091598 A091599 this_sequence A091601 A091602 A091603
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Jan 23 2004
|
|
|
Search completed in 0.002 seconds
|
