|
%I M5319 N2312 #27 Feb 10 2016 03:44:12
%S 60,720,6090,47040,363384,2913120,24560910,218386080,2044958916,
%T 20112075984,207161237010,2228884869120,24989300398320,
%U 291322535242176,3524580157816854,44176838981652000,572725044049055100,7668896804089696560,105920137922879314650,1507138839384235136640,22068265782102952223400,332178010291171425732000,5135009134117954527323550,81449458937043220255508640
%N Number of labeled trees of diameter 4 with n nodes.
%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 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>
%F a(n)=A000551(n)-n*(n-1)*(2^(n-2)-1). - _Sean A. Irvine_, Nov 22 2010
%t a[n_] = n(n-1)(Sum[k^(n-k-2)*Binomial[n-2, k-1], {k, n-2}] - 2^(n-2) + 1); Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, Feb 10 2016, after _Sean A. Irvine_ *)
%K nonn
%O 5,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 22 2010
|
