OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 60
FORMULA
E.g.f.: x*exp(x*exp(x*exp(x*exp(x)))).
MAPLE
spec := [S, {T2=Prod(Z, Set(T3)), S=Prod(Z, Set(T1)), T4=Z, T3=Prod(Z, Set(T4)), T1=Prod(Z, Set(T2))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x*Exp[x*Exp[x*Exp[x*Exp[x]]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 23 2018 *)
PROG
(PARI) my(x='x+O('x^20)); concat(0, Vec(serlaplace( x*exp(x*exp(x*exp(x*exp(x)))) ))) \\ G. C. Greubel, May 13 2019
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( x*Exp(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*exp(x)))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 13 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Added "at most" in the title; by Stanislav Sykora, May 12 2012
STATUS
approved