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A000406
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Coefficients of iterated exponentials.
(Formerly M4264 N1782)
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8
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1, 6, 57, 741, 12244, 245755, 5809875, 158198200, 4877852505, 168055077875, 6400217406500, 267058149580823, 12118701719205803, 594291742526530761, 31323687504696772151, 1766116437541895988303, 106080070002238888908150
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OFFSET
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1,2
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REFERENCES
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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).
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LINKS
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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 302
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FORMULA
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E.g.f.: -log(1+log(1+log(1+log(1+log(1+log(1-x)))))).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A003713, A000268, A000310, A000359, A001765.
Sequence in context: A087659 A107718 A308863 * A305276 A032119 A294511
Adjacent sequences: A000403 A000404 A000405 * A000407 A000408 A000409
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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