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 A000555 Number of labeled trees of diameter 4 with n nodes. (Formerly M5319 N2312) 0
 60, 720, 6090, 47040, 363384, 2913120, 24560910, 218386080, 2044958916, 20112075984, 207161237010, 2228884869120, 24989300398320, 291322535242176, 3524580157816854, 44176838981652000, 572725044049055100, 7668896804089696560, 105920137922879314650, 1507138839384235136640, 22068265782102952223400, 332178010291171425732000, 5135009134117954527323550, 81449458937043220255508640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. FORMULA a(n)=A000551(n)-n*(n-1)*(2^(n-2)-1). - Sean A. Irvine, Nov 22 2010 MATHEMATICA 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 *) CROSSREFS Sequence in context: A088945 A269189 A136008 * A034865 A138409 A024016 Adjacent sequences:  A000552 A000553 A000554 * A000556 A000557 A000558 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Nov 22 2010 STATUS approved

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Last modified February 17 18:13 EST 2020. Contains 332000 sequences. (Running on oeis4.)