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Search: id:A135147
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| A135147 |
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A binomial recursion : a(n)=p(n) (see comment). |
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+0
6
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| 1, 4, 25, 188, 1671, 17190, 201125, 2638984, 38390179, 613363466, 10678267425, 201215691660, 4080450217247, 88609322165902, 2051573162708125, 50450534991347216, 1313219083705400475, 36072797094375866898
(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,(2+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)=(3-2*log(2))/(2*log(2)-1)=4.177398899124179661610768...
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PROGRAM
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(PARI) r=1; s=2; 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. A135148, A135149, A135150, A135074, A135075.
Sequence in context: A006348 A051820 A054368 this_sequence A064063 A141371 A060908
Adjacent sequences: A135144 A135145 A135146 this_sequence A135148 A135149 A135150
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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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