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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

Table of n, a(n) for n=5..28.

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Index entries for sequences related to trees

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-Fran├žois 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

N. J. A. Sloane

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.)