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Search: id:A135150
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| A135150 |
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A binomial recursion : a(n)=q(n) (see comment). |
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+0
6
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| 0, 1, 7, 59, 577, 6435, 80731, 1126321, 17306899, 290514275, 5290386805, 103892269503, 2188786203451, 49246871008285, 1178620260610039, 29898497436003155, 801364442718809233, 22629823094599476315
(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,(3+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)=(15*Pi-22)/(52-15*Pi)=5.1524450418835554775446337...
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PROGRAM
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(PARI) r=1; s=3; 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, A135074, A135075.
Sequence in context: A015568 A101487 A099659 this_sequence A077409 A099347 A063969
Adjacent sequences: A135147 A135148 A135149 this_sequence A135151 A135152 A135153
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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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