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COMMENTS
| 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
Determinant of the matrix n X n :
((2n,n^2,0,...,0), (1,2n,n^2,0,...,0), (0,1,2n,n^2,0,...,0),..., (0,...,0,1,2n))
- Michel Lagneau (mn.lagneau2(AT)orange.fr), May 04 2010.
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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
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