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A073398
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Ninth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.
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2
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1, 20, 240, 2200, 16940, 115104, 711040, 4072640, 21930480, 112157760, 549010176, 2587777920, 11802273600, 52287866880, 225756241920, 952486588416, 3935984616960, 15961485957120, 63628396339200, 249702113464320, 965924035135488, 3687247950397440
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OFFSET
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0,2
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (20,-160,600,-660,-2496,7680,1920,-28320,7040, 66560,-14080,-113280,-15360,122880,79872,-42240,-76800,-40960,-10240,-1024).
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FORMULA
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a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073397(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9)*binomial(n-k, k)*2^(n-k).
G.f.: 1/(1-2*x*(1+x))^10.
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MATHEMATICA
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CoefficientList[Series[1/(1-2*x-2*x^2)^10, {x, 0, 30}], x] (* G. C. Greubel, Oct 06 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^10 )); // G. C. Greubel, Oct 06 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-2*x^2)^10 ).list()
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CROSSREFS
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Tenth (m=9) column of triangle A073387.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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