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Search: id:A132437
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| A132437 |
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A binomial recursion : a(n)=q(n) (see comment). |
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1
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| 0, 1, 3, 15, 97, 767, 7175, 77497, 949047, 12993303, 196655437, 3260367539, 58761008087, 1143864229549, 23917992791139, 534642521054391, 12722568903456817, 321112383611040455, 8568150193087139231
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Let z(1)=x and z(n)=1+sum(k=1,n-1,(-1+binomial(n,k))*z(k)), then z(n)=p(n)*x+q(n).
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REFERENCES
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B. Cloitre, Binomial recursions, Pi and log2, in preparation 2007
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FORMULA
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Lim n-->infty p(n)/q(n)=(Pi-2)/(4-Pi)=1.329896183162743847239353...
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PROGRAM
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(PARI) r=1; s=-1; v=vector(120, j, x); for(n=2, 120, g=r+sum(k=1, n-1, (s+binomial(n, k))*v[k]); v[n]=g); z(n)=v[n]; p(n)=polcoeff(z(n), 1); q(n)=polcoeff(z(n), 0); a(n)=p(n);
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CROSSREFS
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Cf. A135147, A135148, A135149, A135150, A135074, A135075.
Adjacent sequences: A132434 A132435 A132436 this_sequence A132438 A132439 A132440
Sequence in context: A079689 A108442 A060148 this_sequence A128081 A046635 A091713
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 20 2007
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