A052513 Number of labeled trees of height at most 3.

0, 1, 2, 9, 64, 505, 4536, 46249, 526352, 6604497, 90466480, 1341571561, 21392282088, 364715915161, 6616327512536, 127187163197865, 2581443127409056, 55143025567270561, 1236226458392407008, 29012548251081127753, 711157579030313374520, 18169564436494014726441

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 59

Formula

E.g.f.: x*exp(x*exp(x*exp(x))).

Maple

spec := [S, {S=Prod(Z, Set(T1)), T2=Prod(Z, Set(T3)), T3=Z, T1=Prod(Z, Set(T2))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

nn=20; a=x Exp[x]; b=x Exp[a]; Range[0, nn]! CoefficientList[Series[x Exp[b], {x, 0, nn}], x]  (* Geoffrey Critzer, Sep 20 2012 *)

Prog

(PARI)
N=33;  x='x+O('x^N);
egf=x*exp(x*exp(x*exp(x)));
v=Vec(serlaplace(egf));
vector(#v+1, n, if(n==1, 0, v[n-1]))
/* Joerg Arndt, Sep 15 2012 */
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( x*Exp(x*Exp(x*Exp(x))) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, May 13 2019
(Sage) m = 20; T = taylor(x*exp(x*exp(x*exp(x))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 13 2019

Crossrefs

Cf. A000552.

Cf. A052514 (height at most 4).

Sequence in context: A167913 A076944 A074181 * A216839 A024720 A289717

Adjacent sequences: A052510 A052511 A052512 * A052514 A052515 A052516

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved