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Search: id:A069943
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| A069943 |
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Let b(1)=b(2)=1, b(n+2)=(1/(n+1))*(b(n+1)+b(n)); then a(n)=numerator(b(n)). |
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3
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| 1, 1, 1, 2, 5, 13, 19, 29, 191, 131, 1187, 2231, 17519, 71063, 29881, 323423, 2887921, 13237457, 2397389, 15030317, 742458253, 3748521653, 9670072483, 25451905333, 10932619111, 78684575461, 4163946939067, 11799518538967, 136025604432743
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OFFSET
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1,4
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COMMENT
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Sum(k=1,infinity,b(k))=e^(3/2) where e=2,718... More generally if b(1)=b(2)=...=b(m)=1 and b(n+m+1)=1/(n+m)*(b(n+m)+b(n+m-1)+...+b(n)) then Sum(k=1,infinity,b(k))=e^H(m) where H(m)=1+1/2+1/3+...+1/m is the m-th harmonic number (Benoit Cloitre and Boris Gourevitch).
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FORMULA
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Numerators in the power series of exp(x+x^2/2) (EGF for involutions, cf. A000085). exp(x+x^2/2) = 1 + x + x^2 + 2/3*x^3 + 5/12*x^4 + 13/60*x^5 + 19/180*x^6 + 29/630*x^7 + 191/10080*x^8 + ... - Joerg Arndt (arndt(AT)jjj.de), May 10 2008
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CROSSREFS
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Cf. A069944.
a(n)/A069944(n) = A000085(n-1)/A000142(n-1) in lowest terms. (Christian G. Bower, Jan 14 2006).
Adjacent sequences: A069940 A069941 A069942 this_sequence A069944 A069945 A069946
Sequence in context: A019390 A073770 A077545 this_sequence A002540 A068374 A068371
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2002
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