The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A206855 The sum of the degree of each root node over all rooted labeled trees on n nodes. 0
 0, 0, 2, 12, 96, 1000, 12960, 201684, 3670016, 76527504, 18000000000, 47158953820, 1362182012928, 43011849456888, 1474041721757696, 54493461914062500, 2161727821137838080, 91597537648314105376, 4128944057284204560384, 197293926880252878693804, 9961472000000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The mean root degree approaches 2 as n -> infinity. LINKS Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 179. FORMULA a(n) = Sum_{k=0..n} A206429(n,k)*k. E.g.f.: T(x)^2 where T(x) is the e.g.f. for A000169. a(n) = 2*(n^(n-1) - n^(n-2)). a(n) = 2*A053506(n). - R. J. Mathar, Nov 07 2014 MATHEMATICA nn=15; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; D[ Range[0, nn]!CoefficientList[Series[x Exp[y t], {x, 0, nn}], x], y]/.y->1 CROSSREFS Sequence in context: A052564 A014297 A193425 * A219119 A052611 A340938 Adjacent sequences:  A206852 A206853 A206854 * A206856 A206857 A206858 KEYWORD nonn,easy AUTHOR Geoffrey Critzer, Feb 13 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)