A000238 Number of oriented trees with n nodes. (Formerly M2756 N1108)

1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, 492180, 2266502, 10598452, 50235931, 240872654, 1166732814, 5702001435, 28088787314, 139354922608, 695808554300, 3494390057212, 17641695461662, 89495023510876, 456009893224285, 2332997330210440

Offset

1,3

References

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

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

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

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

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 350 terms from N. J. A. Sloane)

H. R. Afshar, E. A. Bergshoeff, W. Merbis, Interacting spin-2 fields in three dimensions, arXiv preprint arXiv:1410.6164 [hep-th], 2014-2015, JHEP 2015 (2015) # 040.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy), TOC

R. J. Mathar, Oriented trees A000238

R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104.

Index entries for sequences related to trees

Formula

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.

a(n) ~ c * d^n / n^(5/2), where d = A245870 = 5.64654261623294971289271351621..., c = 0.22571615379282714232305... . - Vaclav Kotesovec, Dec 08 2014

Maple

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

Mathematica

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 *)

Prog

(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

Crossrefs

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

Diagonal of A335362.

Sequence in context: A374570 A047153 A281347 * A259811 A148841 A148842

Adjacent sequences: A000235 A000236 A000237 * A000239 A000240 A000241

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

2 errors corrected by Paul Zimmermann, Mar 01 1996

More terms from N. J. A. Sloane, Mar 10 2007

Status

approved