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 A052316 Number of labeled rooted trees with n nodes and 2-colored internal (non-leaf) nodes. 3
 1, 4, 30, 344, 5370, 106452, 2562182, 72592816, 2367054450, 87320153900, 3595646533182, 163492924997448, 8136172620013802, 439858024910227588, 25670670464821310070, 1608575860476990991712, 107716675117341985862370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS N. J. A. Sloane, Transforms FORMULA Divides by 2n and shifts left under exponential transform. E.g.f.: -x-LambertW(-2*x*exp(-x)). - Vladeta Jovovic, Sep 17 2003 a(n) = sum(j=1..n, j^(n-1)*2^j*(-1)^(n-j)*binomial(n,j)), n>1, a(1)=1. - Vladimir Kruchinin, Jan 24 2012 a(n) ~ sqrt(1+LambertW(-exp(-1)/2)) * n^(n-1) / (exp(n)*(-LambertW(-exp(-1)/2))^n). - Vaclav Kotesovec, Oct 05 2013 MATHEMATICA a[n_] := Sum[j^(n-1)*2^j*(-1)^(n-j)*Binomial[n, j], {j, 1, n}]; a[1] = 1; Table[a[n], {n, 1, 17}] (* Jean-François Alcover, Feb 26 2013, after Vladimir Kruchinin *) PROG (Maxima) a(n):=if n=1 then 1 else sum(j^(n-1)*2^j*(-1)^(n-j)*binomial(n, j), j, 1, n); \\ Vladimir Kruchinin, Jan 24 2012 CROSSREFS Cf. A004113, A004114, A052317. Sequence in context: A292220 A099712 A209440 * A089918 A132622 A218296 Adjacent sequences:  A052313 A052314 A052315 * A052317 A052318 A052319 KEYWORD nonn,eigen AUTHOR Christian G. Bower, Dec 15 1999 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)