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%I #19 Dec 29 2014 19:26:06
%S 1,4,18,80,367,1708,8122,39204,191963,950984,4759626,24030736,
%T 122258314,626162464,3225926450,16706775984,86928097451,454203897192,
%U 2382255252398,12537764465072,66193294753768,350472816969976,1860542261745782,9901018433270812
%N Number of oriented trees rooted at an arc.
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 61, (3.3.7).
%H Vincenzo Librandi, <a href="/A063881/b063881.txt">Table of n, a(n) for n = 2..100</a>
%F a(n) = A000151(n)- A000238(n). G.f.: A(x) = B(x)^2, where B(x) is g.f. for A000151.
%p B:= proc(n) option remember; if n<=1 then unapply(x,x) else unapply(convert(series(x*exp(2*sum(B(n-1)(x^k)/k, k=1..n-1)), x,n+1), polynom),x) fi end: a:= proc(n) local T; T:=B(n-1)(x); add(coeff(T,x,k)* coeff(T,x,n-k), k=1..n-1) end: seq(a(n), n=2..23); # _Alois P. Heinz_, Aug 23 2008
%t B[n_ /; n <= 1] = Identity; B[n_] := B[n] = Function[x, Evaluate[Normal[Series[x*Exp[2*Sum[B[n-1][x^k]/k, {k, 1, n-1}]], {x, 0, n+1}]]]]; a[n_] := Module[{T}, T = B[n-1][x]; Sum[Coefficient[T, x, k]*Coefficient[T, x, n-k], {k, 1, n-1}]]; Table[a[n], {n, 2, 23}] (* _Jean-François Alcover_, Feb 17 2014, after _Alois P. Heinz_ *)
%Y Cf. A000151, A000238.
%K nonn
%O 2,2
%A _Vladeta Jovovic_, Aug 27 2001
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