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A000359
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Coefficients of iterated exponentials.
(Formerly M3991 N1654)
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13
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1, 5, 40, 440, 6170, 105315, 2120610, 49242470, 1296133195, 38152216495, 1242274374380, 44345089721923, 1722416374173854, 72330102999829054, 3265871028909088036, 157797437377747327987, 8124524883679977475839, 444098724261935142753430
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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 301
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FORMULA
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E.g.f.: -log(1+log(1+log(1+log(1+log(1-x))))).
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MATHEMATICA
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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 *)
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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, 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
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CROSSREFS
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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
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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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