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A003713
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E.g.f.: ln(1/(1+ln(1-x))).
(Formerly M1799 N0710)
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10
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0, 1, 2, 7, 35, 228, 1834, 17582, 195866, 2487832, 35499576, 562356672, 9794156448, 186025364016, 3826961710272, 84775065603888, 2011929826983504, 50929108873336320, 1369732445916318336, 39005083331889816960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n+1) is the permanent of the n X n matrix M with M(i,i) = i+1, other entries 1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2005
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 34
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 298
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FORMULA
| Sum_{k=1..n} (k-1)!*|Stirling1(n, k)|. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 14 2003
a(n+1) = n! * Sum_{k=0..n} A007840(k)/k!. E.g. a(4) = 228 = 24*(1/1+1/1+3/2+14/6+88/24) = 24+24+36+56+88. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 10 2003
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MAPLE
| series(ln(1/(1+ln(1-x))), x, 17);
with (combstruct): M[ 1798 ] := [ A, {A=Cycle(Cycle(Z))}, labeled ]:
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MATHEMATICA
| Log[ 1/(1+Log[ 1-x ]) ]
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PROG
| (PARI) a(n)=if(n<0, 0, n!*polcoeff(-log(1+log(1-x+x*O(x^n))), n))
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CROSSREFS
| a(n)=|A039814(n, 1)| (first column of triangle). Cf. A000268, A000310, A000359, A000406, A001765.
Cf. A007840.
Sequence in context: A006947 A014307 A000154 * A058129 A101514 A196857
Adjacent sequences: A003710 A003711 A003712 * A003714 A003715 A003716
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. H. Hardin (rhhardin(AT)att.net), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Thanks to Paul Zimmermann for comments.
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