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A000268 E.g.f.: -log(1+log(1+log(1-x))).
(Formerly M3003 N1218)
8
1, 3, 15, 105, 947, 10472, 137337, 2085605, 36017472, 697407850, 14969626900, 352877606716, 9064191508018, 252024567201300, 7542036496650006, 241721880399970938, 8261159383595659128, 299916384730043070880 (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 299

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

FORMULA

a(n) = sum((m-1)!*(-1)^(n+m)*sum(stirling1(n, k)*stirling1(k, m), k,m,n), m,1,n), n>0. - Vladimir Kruchinin, Sep 14 2010

MATHEMATICA

max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 - x]]]/x + O[x]^max, x] * Range[max]! (* Jean-François Alcover, Feb 06 2016 *)

PROG

(PARI) a(n) = sum(m=1, n, (m-1)!*(-1)^(n+m)*sum(k=m, n, stirling(n, k, 1)*stirling(k, m, 1))); \\ Michel Marcus, Feb 06 2016

CROSSREFS

a(n)=|A039815(n, 1)| (first column of triangle).

Cf. A003713, A000310, A000359, A000406, A001765.

Sequence in context: A251598 A247304 A001147 * A207818 A118750 A070826

Adjacent sequences:  A000265 A000266 A000267 * A000269 A000270 A000271

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Revised description from Christian G. Bower, Aug 15 1998

STATUS

approved

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Last modified December 10 15:13 EST 2016. Contains 279003 sequences.