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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 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 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 Cf. A003713, A000268, A000310, A000359, A001765. Sequence in context: A087659 A107718 A308863 * A305276 A032119 A294511 Adjacent sequences: A000403 A000404 A000405 * A000407 A000408 A000409 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)