A000310 Coefficients of iterated exponentials. (Formerly M3612 N1464)

1, 4, 26, 234, 2696, 37919, 630521, 12111114, 264051201, 6445170229, 174183891471, 5164718385337, 166737090160871, 5822980248613990, 218756388226681557, 8797723991458469015, 377159237609540937788, 17170729962232112834302, 827382365085791968518198, 42070004707327023844695198

Offset

1,2

References

J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.

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

T. D. Noe, Table of n, a(n) for n=1..100

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Jekuthiel Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 300

Formula

E.g.f.: -log(1+log(1+log(1+log(1-x)))).

Mathematica

max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 + Log[1 - x]]]]/x + O[x]^max, x]*Range[max]! (* Jean-François Alcover, Feb 07 2016 *)

Prog

(PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, abs(stirling(n, j, 1))*T(j, k-1)));
a(n) = T(n, 4); \\ Seiichi Manyama, Feb 11 2022
(PARI) my(x='x+O('x^40)); Vec(serlaplace(-log(1+log(1+log(1+log(1-x)))))); \\ Michel Marcus, Feb 11 2022

Crossrefs

a(n) = |A039816(n, 1)| (first column of triangle). Cf. A003713, A000268, A000359, A000406, A001765.

Sequence in context: A227917 A136227 A346978 * A054360 A124824 A000311

Adjacent sequences: A000307 A000308 A000309 * A000311 A000312 A000313

Keyword

nonn

Author

N. J. A. Sloane

Status

approved