A000406 Coefficients of iterated exponentials. (Formerly M4264 N1782)

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

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 302

Formula

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

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 *)

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, 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

Crossrefs

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

Sequence in context: A369071 A107718 A308863 * A305276 A032119 A294511

Adjacent sequences: A000403 A000404 A000405 * A000407 A000408 A000409

Keyword

nonn

Author

N. J. A. Sloane

Status

approved