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A069944
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a(n) = denominator(b(n)), where b(1) = b(2) = 1, b(n) = (b(n-1) + b(n-2))/(n-1).
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3
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1, 1, 1, 3, 12, 60, 180, 630, 10080, 18144, 453600, 2494800, 59875200, 778377600, 1089728640, 40864824000, 1307674368000, 22230464256000, 15390321408000, 380140938777600, 76028187755520000, 1596591942865920000
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OFFSET
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1,4
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COMMENTS
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Sum_{k >= 1} b(k) = e^(3/2) where e = 2.718... . More generally if b(1) = b(2) = ... = b(m) = 1 and b(n+m+1) = 1/(n+m)*( b(n+m) + b(n+m-1) + ... + b(n) ) then Sum_{k >= 1} b(k) = e^H(m) where H(m) = Sum_{j=1..m} 1/j is the m-th harmonic number (Benoit Cloitre and Boris Gourevitch).
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LINKS
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FORMULA
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MATHEMATICA
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Table[Denominator[n*(-I/Sqrt[2])^(n-1)*HermiteH[n-1, I/Sqrt[2]]/n!], {n, 30}] (* G. C. Greubel, Aug 17 2022 *)
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PROG
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(Magma)
A013989:= func< n | (&+[Factorial(n)/(2^k*Factorial(n-2*k)*Factorial(k)): k in [0..Floor(n/2)]]) >;
(SageMath)
@CachedFunction
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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