%I M3083 #21 Jun 29 2017 19:29:20
%S 1,3,21,231,3495,67455,1584765,43897455,1400923755,50619052575,
%T 2042745514425,91066568444775,4444738893770175,235731740255186175,
%U 13499365993279291125,830161812269496081375,54564569247212367217875,3817309552613869238301375
%N A class of rooted trees with n nodes.
%C See Table 3 on page 32 of the Felsenstein reference: "The numbers of rooted trees with n labelled species, allowing some interior nodes to be labelled, but allowing no more than two immediate descendants of each interior node." - _Joerg Arndt_, Jun 02 2016
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Felsenstein, <a href="http://www.jstor.org/stable/2412810">The number of evolutionary trees</a>, Systematic Zoology, 27 (1978), 27-33.
%H J. Felsenstein, <a href="/A005373/a005373.pdf">The number of evolutionary trees</a>, Systematic Zoology, 27 (1978), 27-33. (Annotated scanned copy)
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = Sum_{m=1..n} Sum_{p=1..n-m} V(n,m,p) where V(1,0,0)=1, V(1,i,j)=0, and V(n,m,p) = [p>0]*((2*n-2*m-p-2)*V(n-1,m,p1) + (n-m-p)*V(n-1,m,p-1)) + [m>0]*((n-2*m-p)*V(n-1,m-1,p) + (p+1)*V(n-1,m-1,p+1)) + [2*n-2*m-p-3>0]*(2*n-2*m-p-3)*V(n-1,m,p) with [t>0]=1 if t>0 and 0 otherwise. - _Sean A. Irvine_, Jun 02 2016
%K nonn
%O 1,2
%A _N. J. A. Sloane_.
%E More terms from _Sean A. Irvine_, Jun 02 2016