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Search: id:A096050
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| A096050 |
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Decimal expansion of limit n-->infty B(2n,7)/(B(2n)*49^n) ( see comment for B(n,k) definition ). |
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+0
3
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| 1, 0, 6, 2, 7, 5, 1, 6, 9, 9, 6, 9, 0, 2, 1, 1, 0, 7, 8, 2, 4, 5, 8, 3, 2, 5, 1, 9, 3, 3, 2, 6, 2, 6, 6, 9, 8, 2, 2, 7, 9, 5, 4, 2, 1, 1, 5, 1, 7, 2, 6, 6, 3, 1, 5, 7, 7, 2, 4, 0, 8, 4, 2, 6, 8, 1, 7, 1, 9, 1, 0, 5, 7, 9, 2, 3, 9, 1, 8, 7, 8, 5, 9, 0, 4, 0, 0, 9, 5, 8, 2, 1, 1, 2, 2, 3, 5, 7, 7, 1, 3, 8, 8, 8, 2
(list; cons; graph; listen)
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OFFSET
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1,3
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COMMENT
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B(n,p)=sum(i=0,n,p^i*sum(j=0,i,binomial(n,j)*B(j))) where B(k)=k-th Bernoulli number. B(2n,p)/B(2n) take integer values for all n if p=1,2,3,4,6. p=5 is the smallest integer for which B(2n,5)/B(2n) is not always integer valued. And limit n-->infty B(2n,5)/(B(2n)*25^n) =(21-sqrt(5))/16
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FORMULA
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limit n-->infty B(2n, 7)/(B(2n)*49^n) = 1.0627516996902110782... the smallest root of 1728*X^3 - 6192*X^2 + 7368*X - 2911=0
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PROGRAM
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(PARI) solve(q=1, 1.1, 1728*q^3-6192*q^2+7368*q-2911)
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CROSSREFS
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Cf. A096045, A096046, A096047, A096048, A096049.
Sequence in context: A002371 A048595 A153313 this_sequence A115731 A163340 A021090
Adjacent sequences: A096047 A096048 A096049 this_sequence A096051 A096052 A096053
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KEYWORD
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cons,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2004
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