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Search: id:A002104
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| A002104 |
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Logarithmic numbers.
(Formerly M2749 N1105)
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+0
11
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| 1, 3, 8, 24, 89, 415, 2372, 16072, 125673, 1112083, 10976184, 119481296, 1421542641, 18348340127, 255323504932, 3809950977008, 60683990530225, 1027542662934915, 18430998766219336, 349096664728623336
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Prime p divides a(p+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
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REFERENCES
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J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
J. C. Tiernan, An efficient search algorithm to find the elementary circuits of a graph, Commun. ACM, 13 (1970), 722-726.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
Index entries for sequences related to logarithmic numbers
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 116
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FORMULA
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E.g.f.: -exp(x)*ln(1-x). a(n) = Sum_{k=1..n} Sum_{i=0..n-k} (n-k)!/i!.
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.
a(n+1)-a(n)=A000522(n)
a(n)=sum{k=0..n-1, binomial(n, k)*(n-k-1)!} - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004
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
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MATHEMATICA
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Table[Sum[Sum[m!/k!, {k, 0, m}], {m, 0, n-1}], {n, 1, 30}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
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CROSSREFS
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Cf. A006231.
Cf. A001338.
Sequence in context: A125655 A134165 A071016 this_sequence A102919 A102476 A123638
Adjacent sequences: A002101 A002102 A002103 this_sequence A002105 A002106 A002107
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001
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