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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; text; 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).

LINKS

Table of n, a(n) for n=0..25.

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: A055206 A216614 A146757 * A056037 A125903 A268644

Adjacent sequences:  A091132 A091133 A091134 * A091136 A091137 A091138

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 22 2004

STATUS

approved

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Last modified October 23 13:15 EDT 2018. Contains 316528 sequences. (Running on oeis4.)