A000359 Coefficients of iterated exponentials.

1, 5, 40, 440, 6170, 105315, 2120610, 49242470, 1296133195, 38152216495, 1242274374380, 44345089721923, 1722416374173854, 72330102999829054, 3265871028909088036, 157797437377747327987, 8124524883679977475839, 444098724261935142753430

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 301

Crossrefs

a(n) = |A039817(n, 1)| (first column of triangle). Cf. A003713, A000268, A000310, A000406, A001765.

Programs

Mathematica

max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 + Log[1 + Log[1 - x]]]]]/x + O[x]^max, x]*Range[max]! (* Jean-François Alcover, Feb 08 2016 *)

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, 5); \\ 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-x))))))) \\ Seiichi Manyama, Feb 11 2022

Formula

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