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A091600 Expansion of solution to xA(x)(A(x)-x+1)=A(xA(x)). 0
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; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..30.

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

Sequence in context: A257104 A318008 A199410 * A261232 A176334 A257386

Adjacent sequences:  A091597 A091598 A091599 * A091601 A091602 A091603

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 23 2004

STATUS

approved

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Last modified January 18 12:44 EST 2021. Contains 340254 sequences. (Running on oeis4.)