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A099044
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a(n) = (2*0^n + 3^n*binomial(2*n,n))/3.
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3
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1, 2, 18, 180, 1890, 20412, 224532, 2501928, 28146690, 318995820, 3636552348, 41655054168, 479033122932, 5527305264600, 63958818061800, 741922289516880, 8624846615633730, 100454095876204620, 1171964451889053900, 13693479385229998200, 160213708807190978940
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OFFSET
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0,2
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COMMENTS
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(1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.
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LINKS
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FORMULA
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G.f.: 1/3 + 4*x/(sqrt(1-12*x)(1-sqrt(1-12*x))) = (1 + 2*sqrt(1-12*x))/(3*sqrt(1-12*x)).
E.g.f.: (2 + exp(6*x) * BesselI(0,6*x)) / 3. - Ilya Gutkovskiy, Nov 17 2021
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MATHEMATICA
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Join[{1}, Table[3^(n-1)*binomial(2*n, n), {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)
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PROG
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(Magma) [(2*0^n + 3^n*Binomial(2*n, n))/3: n in [ 0..20]]; // Vincenzo Librandi, Nov 24 2012
(PARI) for(n=0, 30, print1((2*0^n + 3^n*binomial(2*n, n))/3, ", ")) \\ G. C. Greubel, Dec 31 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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