OFFSET
0,5
COMMENTS
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, Jul 27 2007
FORMULA
G.f. A(x) satisfies A(x)= x +(A(x*A(x))-x*A(x))/(x*A(x)).
PROG
(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
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 23 2004
STATUS
approved