OFFSET
0,3
COMMENTS
Also number of ordered trees with n edges that have no vertices of outdegree 4.
FORMULA
G.f.: G=G(z) satisfies z^5*G^5-z^4*G^4+zG^2-G+1=0.
a(n) = 1/n*sum(j=ceiling((3*n+2)/5)..n, C(n,j)*C(5*j-3*n-2,j-1) * (-1)^(n-j)), n>0. [From Vladimir Kruchinin, Mar 07 2011]
EXAMPLE
a(4) = 13 because among the Catalan(4)=14 Dyck paths of semilength 4 only UUUUDDDD has an ascent of length 4 (here U=(1,1), D=(1,-1)).
MAPLE
Order:=35: Y:=solve(series((Y-Y^2)/(1-Y^4+Y^5), Y)=z, Y): seq(coeff(Y, z^n), n=1..30); #(Y=zG)
PROG
(Maxima) a114509(n):= 1/n*sum(binomial(n, j)*binomial(5*j-3*n-2, j-1)* (-1)^(n-j), j, ceiling((3*n+2)/5), n); [Vladimir Kruchinin, Mar 07 2011]
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 03 2005
STATUS
approved