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Search: id:A007440
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| A007440 |
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Reversion of g.f. for Fibonacci numbers 1,1,2,3,5,...
(Formerly M0413)
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+0
8
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| 1, -1, 0, 2, -3, -1, 11, -15, -13, 77, -86, -144, 595, -495, -1520, 4810, -2485, -15675, 39560, -6290, -159105, 324805, 87075, -1592843, 2616757, 2136539, -15726114, 20247800, 32296693, -152909577, 145139491, 417959049, -1460704685, 885536173, 4997618808, -13658704994
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Binomial transform of A104565 (reversion of Pell numbers). - Paul Barry (pbarry(AT)wit.ie), Mar 15 2005
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LINKS
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Index entries for reversions of series
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FORMULA
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(n + 3)*a(n + 2) = -(2*n + 3)*a(n + 1) - 5*n*a(n), a(1) = 1, a(2) = -1.
G.f.: (-1-x+sqrt(1+2x+5x^2))/(2x).
a(n)=sum{k=0..floor(n/2), binomial(n, 2k)*C(k)*(-1)^(n-k)}, where C(n) is A000108. - Paul Barry (pbarry(AT)wit.ie), May 16 2005
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PROGRAM
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(PARI) a(n)=polcoeff((-1-x+sqrt(1+2*x+5*x^2+x^2*O(x^n)))/(2*x), n)
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CROSSREFS
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Cf. A000045.
Sequence in context: A009026 A046222 A074307 this_sequence A100223 A129969 A104379
Adjacent sequences: A007437 A007438 A007439 this_sequence A007441 A007442 A007443
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KEYWORD
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sign
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AUTHOR
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njas
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EXTENSIONS
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Extended and signs added by Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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