1,2

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

F. Ellermann, Illustration of binomial transforms

Index entries for sequences related to rooted trees

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

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

Adjacent sequences: A055894 A055895 A055896 this_sequence A055898 A055899 A055900

Sequence in context: A141133 A036077 A080446 this_sequence A052563 A007724 A126778

nonn

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

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