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A063881 Number of oriented trees rooted at an arc. 1
1, 4, 18, 80, 367, 1708, 8122, 39204, 191963, 950984, 4759626, 24030736, 122258314, 626162464, 3225926450, 16706775984, 86928097451, 454203897192, 2382255252398, 12537764465072, 66193294753768, 350472816969976, 1860542261745782, 9901018433270812 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 61, (3.3.7).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..100

FORMULA

a(n) = A000151(n)- A000238(n). G.f.: A(x) = B(x)^2, where B(x) is g.f. for A000151.

MAPLE

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

MATHEMATICA

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-Fran├žois Alcover, Feb 17 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A000151, A000238.

Sequence in context: A257390 A104631 A106391 * A264004 A282708 A252823

Adjacent sequences:  A063878 A063879 A063880 * A063882 A063883 A063884

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Aug 27 2001

STATUS

approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)