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A372015
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Product of Fibonacci and self-convolution of Fibonacci numbers: a(n) = A000045(n+1)*A001629(n+1).
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0
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0, 1, 4, 15, 50, 160, 494, 1491, 4420, 12925, 37380, 107136, 304764, 861445, 2421700, 6775755, 18879734, 52413856, 145038890, 400183575, 1101277060, 3023462521, 8282790024, 22646131200, 61805595000, 168399404425, 458128878724, 1244567262471, 3376576740410, 9149594423200
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = F(n+1)*((n+2)*F(n) + (n)*F(n+2))/5 where F(n) = A000045(n) is the Fibonacci numbers.
G.f.: x*(1-x)/((1+x)*(1-3*x+x^2)^2).
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MAPLE
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a := proc(n) option remember; if n < 3 then return n^2 fi;
-((2 - 2*n^2 + n)*a(n - 1) + (1 - 2*n^2 + 3*n)*a(n - 2) + n^2*a(n - 3))/(n - 1)^2 end: seq(a(n), n = 0..29); # Peter Luschny, Apr 16 2024
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MATHEMATICA
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CoefficientList[Series[x(1-x)/((1+x)*(1-3*x+x^2)^2), {x, 0, 29}], x] (* Stefano Spezia, Apr 16 2024 *)
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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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STATUS
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approved
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