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A055897 n*(n-1)^(n-1). +0
4
1, 2, 12, 108, 1280, 18750, 326592, 6588344, 150994944, 3874204890, 110000000000, 3423740047332, 115909305827328, 4240251492291542, 166680102383370240, 7006302246093750000, 313594649253062377472 (list; graph; listen)
OFFSET

1,2

COMMENT

Total number of leaves in all labeled rooted trees with n nodes.

Number of endofunctions of [n] such that no element of [n-1] is fixed. E.g. a(3)=12: 123 -> 331, 332, 333, 311, 312, 313, 231, 232, 233, 211, 212, 213.

Number of functions f: {1, 2, ..., n} --> {1, 2, ..., n} such that f(1) != f(2), f(2) != f(3), ..., f(n-1) != f(n). - Warut Roonguthai (warut822(AT)yahoo.com), May 06 2006

LINKS

F. Ellermann, Illustration of binomial transforms

Index entries for sequences related to rooted trees

FORMULA

E.g.f.: x/(1-T), where T=T(x) is Euler's tree function (see A000169).

a(n) = sum{k=1 to n} (A055302(n, k)*k).

a(n) = the n-th term of the (n-1)-th binomial transform of {1, 1, 4, 18, 96, .., (n-1)*(n-1)!, ..} (cf. A001563); a(n) = (n-1)^(n-1) + sum_{i=2..n} (n-1)^(n-i)*C(n-1, i-1)*(i-1)*(i-1)!). - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 17 2003

CROSSREFS

Cf. A003227, A003228, A055314, A055540, A055541, A060226, A118537.

Sequence in context: A141133 A036077 A080446 this_sequence A052563 A007724 A126778

Adjacent sequences: A055894 A055895 A055896 this_sequence A055898 A055899 A055900

KEYWORD

nonn

AUTHOR

Christian G. Bower (bowerc(AT)usa.net), Jun 12 2000

EXTENSIONS

Additional comments from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 31 2001 and Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 11 2001

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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