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Search: id:A135074
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| A135074 |
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A binomial recursion : a(n)=p(n) (see comment). |
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+0
8
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| 1, 3, 16, 106, 851, 8044, 87540, 1078177, 14827510, 225228130, 3745187549, 67666969438, 1320018345504, 27651573264631, 619077538462468, 14752261527199414, 372797929345665683, 9958134039336196072
(list; graph; listen)
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OFFSET
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1,2
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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). Lim n-->infty p(n)/q(n)=(3*pi-14)/(8-3*pi)=3.2111824896280692148...
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REFERENCES
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B. Cloitre, Binomial recursions, Pi and log2, in preparation 2007
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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. A135075.
Adjacent sequences: A135071 A135072 A135073 this_sequence A135075 A135076 A135077
Sequence in context: A014304 A063548 A074551 this_sequence A074540 A039751 A141003
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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 17 2007
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