%I M2887 N1158 #31 May 19 2023 04:19:17
%S 1,3,11,29,74,167,367,755,1515,2931,5551,10263,18677,33409,59024,
%T 102984,177915,304458,516939,871180,1458882,2428548,4021670,6627515,
%U 10874462,17770474,28932739,46943967,75925797,122433291,196879385,315759282,505168033,806290796,1284034606,2040485004,3235965074,5121801962,8091411114,12759606939,20085832527,31565046053,49523414558,77575278933,121329065354,189475663960,295465391518,460087656595,715436020515,1110994054004
%N Number of trees of diameter 6.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Christian Sievers, <a href="/A000251/b000251.txt">Table of n, a(n) for n = 7..9286</a>
%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%o (PARI) \\ sh_euler is shifted Euler transform.
%o sh_euler(p)={my(m=serprec(p,x)-1); x*exp(sum(i=1, m, subst(p+O(x^(1+m\i)), x, x^i)/i))}
%o lista(n)={my(s0=x + O(x*x^n), s1=sh_euler(s0), s2=sh_euler(s1), s3=sh_euler(s2), r2=s2-s1, r3=s3-s2, t6=r3-r2*s2); Vec(t6)} \\ _Christian Sievers_, May 18 2023
%Y Cf. A034853, A000550 (diameter 7).
%K nonn
%O 7,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 21 2010