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A206531
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a(n) = (2*(n+1)*(2*n+1)-1)*a(n-1) + 2*n*(2*n-1)*a(n-2), a(0)=0, a(1)=2.
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3
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0, 2, 58, 3250, 292498, 38609738, 7026972314, 1686473355362, 516060846740770, 196103121761492602, 90599642253809582122, 50011002524102889331346, 32507151640666878065374898, 24575406640344159817423422890
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OFFSET
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0,2
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COMMENTS
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The numerators of the fractions limiting to the value of A206533.
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REFERENCES
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E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.
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LINKS
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FORMULA
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MATHEMATICA
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RecurrenceTable[{a[n]==(2(n+1)(2n+1)-1)a[n-1]+2n(2n-1)a[n-2], a[0]==0, a[1]==2}, a, {n, 15}]
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PROG
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(Magma) [n le 2 select 2*(n-1) else (2*n*(2*n-1)-1)*Self(n-1) + 2*(n-1)*(2*n-3)*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 21 2022
(SageMath)
@CachedFunction
if (n<2): return 2*n
else: return (2*(n+1)*(2*n+1)-1)*a(n-1) + 2*n*(2*n-1)*a(n-2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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