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A000406 Coefficients of iterated exponentials.
(Formerly M4264 N1782)
8
1, 6, 57, 741, 12244, 245755, 5809875, 158198200, 4877852505, 168055077875, 6400217406500, 267058149580823, 12118701719205803, 594291742526530761, 31323687504696772151, 1766116437541895988303, 106080070002238888908150 (list; graph; refs; listen; history; text; internal format)
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
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]
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
Sequence in context: A369071 A107718 A308863 * A305276 A032119 A294511
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)