Search: id:A002104
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%I A002104 M2749 N1105
%S A002104 1,3,8,24,89,415,2372,16072,125673,1112083,10976184,119481296,
%T A002104 1421542641,18348340127,255323504932,3809950977008,60683990530225,
%U A002104 1027542662934915,18430998766219336,349096664728623336
%N A002104 Logarithmic numbers.
%C A002104 Prime p divides a(p+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jul 05 2006
%D A002104 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002104 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002104 J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
%D A002104 J. C. Tiernan, An efficient search algorithm to find the elementary circuits 
               of a graph, Commun. ACM, 13 (1970), 722-726.
%H A002104 T. D. Noe, <a href="b002104.txt">Table of n, a(n) for n=1..100</a>
%H A002104 <a href="Sindx_Lo.html#logarithmic">Index entries for sequences related 
               to logarithmic numbers</a>
%H A002104 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=116">
               Encyclopedia of Combinatorial Structures 116</a>
%F A002104 E.g.f.: -exp(x)*ln(1-x). a(n) = Sum_{k=1..n} Sum_{i=0..n-k} (n-k)!/i!.
%F A002104 a(n) = Sum_{k=1..n} n(n-1)...(n-k+1)/k = A006231(n) + n - Avi Peretz 
               (njk(AT)netvision.net.il), Mar 24 2001.
%F A002104 a(n+1)-a(n)=A000522(n)
%F A002104 a(n)=sum{k=0..n-1, binomial(n, k)*(n-k-1)!} - Paul Barry (pbarry(AT)wit.ie), 
               Aug 26 2004
%F A002104 a(n) = Sum[Sum[m!/k!,{k,0,m}],{m,0,n-1}]. a(n) = Sum[A000522(m),{m,0,
               n-1}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
%t A002104 Table[Sum[Sum[m!/k!,{k,0,m}],{m,0,n-1}],{n,1,30}] - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Jul 05 2006
%Y A002104 Cf. A006231.
%Y A002104 Cf. A001338.
%Y A002104 Sequence in context: A125655 A134165 A071016 this_sequence A102919 A102476 
               A057420
%Y A002104 Adjacent sequences: A002101 A002102 A002103 this_sequence A002105 A002106 
               A002107
%K A002104 nonn,easy,nice
%O A002104 1,2
%A A002104 N. J. A. Sloane (njas(AT)research.att.com).
%E A002104 More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001

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