A000555 Number of labeled trees of diameter 4 with n nodes.

60, 720, 6090, 47040, 363384, 2913120, 24560910, 218386080, 2044958916, 20112075984, 207161237010, 2228884869120, 24989300398320, 291322535242176, 3524580157816854, 44176838981652000, 572725044049055100, 7668896804089696560, 105920137922879314650, 1507138839384235136640, 22068265782102952223400, 332178010291171425732000, 5135009134117954527323550, 81449458937043220255508640

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn

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.
• Index entries for sequences related to trees

Programs

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 *)

Formula

a(n)=A000551(n)-n*(n-1)*(2^(n-2)-1). - Sean A. Irvine, Nov 22 2010

Extensions

More terms from Sean A. Irvine, Nov 22 2010