A001765 Coefficients of iterated exponentials.

1, 7, 77, 1155, 21973, 506989, 13761937, 429853851, 15192078027, 599551077881, 26140497946017, 1248134313062231, 64783855286002573, 3632510833677434324, 218845138322691595694, 14099918095287618382033, 967508237903439910445565, 70447525748137979196484589

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
• T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
• 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.
• T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 303

Crossrefs

Cf. A003713, A000268, A000310, A000359, A000406.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[-Log[1+Log[1+Log[1+Log[1+Log[1+Log[1+Log[1-x]]]]]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 07 2023 *)

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, 7); \\ 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+log(1-x))))))))) \\ Seiichi Manyama, Feb 11 2022

Formula

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