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A111262
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a(n)=(1/n)*sum(k=1,n,F(4k)B(2n-2k)binomial(2n,2k)), where F are Fibonacci numbers and B are Bernoulli numbers.
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3
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3, 12, 65, 403, 2652, 17889, 121859, 833260, 5706081, 39096531, 267936188, 1836369217, 12586419075, 86267964108, 591287758337, 4052742230419, 27777897084444, 190392509164065, 1304969593244291, 8944394450283436
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Values are always integers.
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FORMULA
| a(n)=F(4n-2)+2F(2n-1); recurrence : a(n)=10a(n-1)-23a(n-2)+10a(n-3)-a(n-4)
O.g.f.: -x*(-3+18*x-14*x^2+x^3)/((x^2-3*x+1)*(x^2-7*x+1)) = -1+(2-4*x)/(x^2-3*x+1)+(-1+8*x)/(x^2-7*x+1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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PROG
| (PARI) a(n)=fibonacci(4*n-2)+2*fibonacci(2*n-1)
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CROSSREFS
| Cf. A001519.
Sequence in context: A029851 A201720 A196559 * A139134 A200309 A109577
Adjacent sequences: A111259 A111260 A111261 * A111263 A111264 A111265
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 12 2005, corrected Feb 24 2008
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