0,3

Index entries for sequences related to rooted trees

E.g.f.: (4-3*e^x)/(5-4*e^x).

a(n) is asymptotic to (1/20)*n!/log(5/4)^(n+1). More generally if m>1, the number of m-level labeled linear rooted trees with n leaves is asymptotic to n!/log(m/(m-1))^(n+1)/(m^2-m). - Benoit Cloitre, Jan 30 2003

For m-level trees (m>1), e.g.f. is (m-1-(m-2)*e^x)/(m-(m-1)*e^x) and number of trees is 1/(m*(m-1))*sum(k>=0, (1-1/m)^k*k^n). Here m=5, so a(n)=(1/20)*sum(k>=0, (4/5)^k*k^n) (for n>0). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 30 2003

(PARI) a(n)=n!*if(n<0, 0, polcoeff((4-3*exp(x))/(5-4*exp(x))+O(x^(n+1)), n))

Cf. A000670, A050351-A050359.

Equals 1/4 * A094417(n) for n>0.

Sequence in context: A138978 A046184 A084769 this_sequence A112941 A045976 A053889

Adjacent sequences: A050350 A050351 A050352 this_sequence A050354 A050355 A050356

nonn

Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.