%I M2756 N1108 #63 Jun 09 2020 09:22:57

%S 1,1,3,8,27,91,350,1376,5743,24635,108968,492180,2266502,10598452,

%T 50235931,240872654,1166732814,5702001435,28088787314,139354922608,

%U 695808554300,3494390057212,17641695461662,89495023510876,456009893224285,2332997330210440

%N Number of oriented trees with n nodes.

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 286.

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 60, r(x).

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A000238/b000238.txt">Table of n, a(n) for n = 1..1000</a> (first 350 terms from N. J. A. Sloane)

%H H. R. Afshar, E. A. Bergshoeff, W. Merbis, <a href="http://arxiv.org/abs/1410.6164">Interacting spin-2 fields in three dimensions</a>, arXiv preprint arXiv:1410.6164 [hep-th], 2014-2015, <a href="http://doi.org/10.1007/JHEP01(2015)040">JHEP 2015 (2015) # 040</a>.

%H P. Leroux and B. Miloudi, <a href="/A000081/a000081_2.pdf">Généralisations de la formule d'Otter</a>, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy), <a href="https://www.labmath.uqam.ca/~annales/english/volumes/16-1.html">TOC</a>

%H R. J. Mathar, <a href="/A000238/a000238.pdf">Oriented trees A000238</a>

%H R. Simion, <a href="http://dx.doi.org/10.1016/0012-365X(91)90061-6">Trees with 1-factors and oriented trees</a>, Discrete Math., 88 (1991), 93-104.

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F G.f. = x+x^2+3*x^3+8*x^4+27*x^5+... = R(x)-R(x)^2, where R(x) = g.f. for A000151.

%F a(n) ~ c * d^n / n^(5/2), where d = A245870 = 5.64654261623294971289271351621..., c = 0.22571615379282714232305... . - _Vaclav Kotesovec_, Dec 08 2014

%p A:= proc(n) option remember; if n=0 then 0 else unapply(convert(series(x*exp(2* add(A(n-1)(x^k)/k, k=1..n-1)), x=0,n), polynom), x) fi end: a:= n-> coeff(series(A(n+1)(x) *(1-A(n+1)(x)), x=0, n+1), x,n): seq(a(n), n=1..26); # _Alois P. Heinz_, Aug 20 2008

%t A[n_][y_] := A[n][y] = If[n == 0, 0, Normal[Series[x*Exp[2*Sum[A[n-1][x^k]/k, {k, 1, n-1}]], {x, 0, n}] /. x -> y]]; a[n_] := SeriesCoefficient[A[n+1][x]*(1-A[n+1][x]), {x, 0, n}]; Table[a[n], {n, 1, 26}] (* _Jean-François Alcover_, Feb 12 2014, translated from Maple *)

%o (PARI) seq(N) = {my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 2/n * sum(i=1, n, sumdiv(i, d, d*A[d]) * A[n-i+1] ) ); Vec(Ser(A)-x*Ser(A)^2)} \\ _Andrew Howroyd_, May 13 2018

%Y Cf. A000060, A000151, A051437 (linear oriented), A334827 (oriented star-like).

%Y Diagonal of A335362.

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E 2 errors corrected by _Paul Zimmermann_, Mar 01 1996

%E More terms from _N. J. A. Sloane_, Mar 10 2007