Search: id:A050353
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%I A050353
%S A050353 1,1,9,121,2169,48601,1306809,40994521,1469709369,59277466201,
%T A050353 2656472295609,130952452264921,7042235448544569,410269802967187801,
%U A050353 25740278881968596409,1730295054262416751321,124066865052334175027769
%N A050353 Number of 5-level labeled linear rooted trees with n leaves.
%H A050353 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A050353 E.g.f.: (4-3*e^x)/(5-4*e^x).
%F A050353 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
%F A050353 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
%o A050353 (PARI) a(n)=n!*if(n<0,0,polcoeff((4-3*exp(x))/(5-4*exp(x))+O(x^(n+1)),
               n))
%Y A050353 Cf. A000670, A050351-A050359.
%Y A050353 Equals 1/4 * A094417(n) for n>0.
%Y A050353 Sequence in context: A138978 A046184 A084769 this_sequence A112941 A045976 
               A053889
%Y A050353 Adjacent sequences: A050350 A050351 A050352 this_sequence A050354 A050355 
               A050356
%K A050353 nonn
%O A050353 0,3
%A A050353 Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.

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