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A023607
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a(n) = n * Fibonacci(n+1).
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19
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0, 1, 4, 9, 20, 40, 78, 147, 272, 495, 890, 1584, 2796, 4901, 8540, 14805, 25552, 43928, 75258, 128535, 218920, 371931, 630454, 1066464, 1800600, 3034825, 5106868, 8580897, 14398412, 24129160, 40388070, 67527579, 112786496, 188195271
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OFFSET
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0,3
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COMMENTS
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Convolution of Fibonacci numbers and Lucas numbers.
d/dx(1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) = (1 + 4x + 9x^2 + ...). - Gary W. Adamson, Jun 27 2009
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LINKS
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FORMULA
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O.g.f.: x(2x+1)/(1-x-x^2)^2. - Len Smiley, Dec 11 2001
a(n) = n*Sum_{k=0..n} binomial(k,n-k). - Paul Barry, Sep 25 2004
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MAPLE
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n*combinat[fibonacci](n+1) ;
end proc:
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MATHEMATICA
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Times@@@Thread[{Range[0, 50], Fibonacci[Range[51]]}] (* Harvey P. Dale, Mar 08 2011 *)
Table[n*Fibonacci[n + 1], {n, 0, 50}]
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PROG
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(Haskell)
a023607 n = a023607_list !! n
a023607_list = zipWith (*) [0..] $ tail a000045_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Simpler description from Samuel Lachterman (slachterman(AT)fuse.net), Sep 19 2003
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STATUS
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approved
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