A000406 Coefficients of iterated exponentials.

1, 6, 57, 741, 12244, 245755, 5809875, 158198200, 4877852505, 168055077875, 6400217406500, 267058149580823, 12118701719205803, 594291742526530761, 31323687504696772151, 1766116437541895988303, 106080070002238888908150

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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 302

Crossrefs

Cf. A003713, A000268, A000310, A000359, A001765.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[-Log[1+Log[1+Log[1+Log[1+ Log[1+ Log[1- x]]]]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 03 2015 *)

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, 6); \\ Seiichi Manyama, Feb 11 2022

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1+log(1+log(1+log(1+log(1+log(1-x)))))))) \\ Seiichi Manyama, Feb 11 2022

Formula

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