A001765 Coefficients of iterated exponentials. (Formerly M4447 N1882)

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

Offset

1,2

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

Formula

E.g.f.: -log(1+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+Log[1-x]]]]]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 07 2023 *)

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, 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

Crossrefs

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

Sequence in context: A249933 A107866 A034176 * A246460 A222145 A240404

Adjacent sequences: A001762 A001763 A001764 * A001766 A001767 A001768

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved