A063881 Number of oriented trees rooted at an arc.

1, 4, 18, 80, 367, 1708, 8122, 39204, 191963, 950984, 4759626, 24030736, 122258314, 626162464, 3225926450, 16706775984, 86928097451, 454203897192, 2382255252398, 12537764465072, 66193294753768, 350472816969976, 1860542261745782, 9901018433270812

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-François 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