Search: id:A003713
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%I A003713 M1799 N0710
%S A003713 0,1,2,7,35,228,1834,17582,195866,2487832,35499576,562356672,
%T A003713 9794156448,186025364016,3826961710272,84775065603888,2011929826983504,
%U A003713 50929108873336320,1369732445916318336,39005083331889816960
%N A003713 E.g.f.: ln(1/(1+ln(1-x))).
%C A003713 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
%D A003713 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003713 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A003713 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%H A003713 T. D. Noe, <a href="b003713.txt">Table of n, a(n) for n=0..100</a>
%H A003713 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A003713 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=34">
               Encyclopedia of Combinatorial Structures 34</a>
%H A003713 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=298">
               Encyclopedia of Combinatorial Structures 298</a>
%F A003713 Sum_{k=1..n} (k-1)!*|Stirling1(n, k)|. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 14 2003
%F A003713 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
%p A003713 series(ln(1/(1+ln(1-x))),x,17);
%p A003713 with (combstruct): M[ 1798 ] := [ A,{A=Cycle(Cycle(Z))},labeled ]:
%t A003713 Log[ 1/(1+Log[ 1-x ]) ]
%o A003713 (PARI) a(n)=if(n<0,0,n!*polcoeff(-log(1+log(1-x+x*O(x^n))),n))
%Y A003713 a(n)=|A039814(n, 1)| (first column of triangle). Cf. A000268, A000310, 
               A000359, A000406, A001765.
%Y A003713 Cf. A007840.
%Y A003713 Sequence in context: A006947 A014307 A000154 this_sequence A058129 A101514 
               A111908
%Y A003713 Adjacent sequences: A003710 A003711 A003712 this_sequence A003714 A003715 
               A003716
%K A003713 nonn,easy,nice
%O A003713 0,3
%A A003713 N. J. A. Sloane (njas(AT)research.att.com), R. H. Hardin (rhhardin(AT)att.net), 
               Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A003713 Thanks to Paul Zimmermann for comments.

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