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Search: id:A132436
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| A132436 |
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A binomial recursion : a(n)=p(n) (see comment). |
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1
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| 1, 1, 4, 20, 129, 1020, 9542, 103063, 1262134, 17279744, 261531315, 4335950346, 78146040374, 1521220672933, 31808447321848, 711019048106744, 16919695824732249, 427046133330613512, 11394750238551713066
(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.
Sequence in context: A126674 A082032 A140585 this_sequence A038173 A141716 A129102
Adjacent sequences: A132433 A132434 A132435 this_sequence A132437 A132438 A132439
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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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