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Search: id:A124126
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| A124126 |
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a(n)=(1/(3n))*sum(k=1,n,F(8k)*B(2n-2k)*binomial(2n,2k)) where F=Fibonacci numbers and B=Bernoulli numbers. |
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+0
1
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| 7, 168, 5425, 199367, 7890120, 327681361, 14071534535, 618924449640, 27702229113265, 1255905441590279, 57477374413516680, 2648841480448502353, 122698149590393354375, 5704992303566275023912, 265994788806640480586545
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)=(1/(3n))*(F(8n-4)+2*L(4n-2)*5^(n-1)+2*F(2n-1)*3^(2n-1)+U(n)) where L=Lucas numbers and U(n) satisfies the order 2 recursion : U(1)=2, U(2)=24, U(n)=23U(n-1)-121U(n-2)
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PROGRAM
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(PARI) a(n)=(1/3/n)*sum(k=1, n, fibonacci(8*k)*bernfrac(2*n-2*k)*binomial(2*n, 2*k))
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CROSSREFS
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Cf. A111262.
Sequence in context: A012689 A098632 A009807 this_sequence A086373 A012067 A012145
Adjacent sequences: A124123 A124124 A124125 this_sequence A124127 A124128 A124129
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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 29 2006
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