A000359 Coefficients of iterated exponentials. (Formerly M3991 N1654)

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

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 301

Formula

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

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 *)

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, 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

Crossrefs

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

Sequence in context: A304866 A202477 A034000 * A121886 A282190 A052868

Adjacent sequences: A000356 A000357 A000358 * A000360 A000361 A000362

Keyword

nonn

Author

N. J. A. Sloane

Status

approved