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%I M3552 N1440 #39 May 19 2023 04:23:04
%S 1,4,19,66,219,645,1813,4802,12265,30198,72396,169231,387707,871989,
%T 1930868,4215615,9091410,19389327,40944999,85691893,177898521,
%U 366614456,750494796,1526979694,3089556090,6219191608,12460307373,24856533408,49387348955,97765283686,192870793594,379287172272
%N Number of trees of diameter 8.
%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="/A000306/b000306.txt">Table of n, a(n) for n = 9..4442</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)
%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(s2=sh_euler(sh_euler(x+O(x*x^n))), s3=sh_euler(s2), s4=sh_euler(s3), r3=s3-s2, r4=s4-s3, t8=r4-r3*s3); Vec(t8)} \\ _Christian Sievers_, May 18 2023
%Y Cf. A034853.
%K nonn
%O 9,2
%A _N. J. A. Sloane_
%E More terms from _Christian Sievers_, May 18 2023
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