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A154242
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Denominators of the coefficients of the polynomials 1/Sum_{n>=1} x^(n-1)/((2*n)!/n!) = 2*exp(-x/4)*sqrt(x)/ (sqrt(Pi)*erf(sqrt(x)/2)).
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1
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1, 3, 45, 1890, 56700, 748440, 10216206000, 8756748000, 2841962760000, 24946749107280000, 8232427205402400000, 103279541304139200000, 3101484625363300176000000, 1431454442475369312000000
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = denominator([x^n]*(1/Sum_{k>=1} x^(k-1)/((2*k)!/k!)).
a(n) = denominator([x^n]*2*exp(-x/4)*sqrt(x)/(sqrt(Pi)*erf(sqrt(x)/2)))).
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MATHEMATICA
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p[x] := FullSimplify[1/Sum[x^(n - 1)/((2*n)!/n!), {n, 1, Infinity}]];
Table[ Denominator[SeriesCoefficient[Series[p[x], {x, 0, 30}], n]], {n, 0, 30}]
Table[Denominator[SeriesCoefficient[Series[2*Exp[-x/4]*Sqrt[x]/(Sqrt[Pi]*Erf[Sqrt[x]/2]), {x, 0, 30}], n]], {n, 0, 50}] (* G. C. Greubel, Sep 07 2016 *)
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PROG
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(PARI) seq(n)={[denominator(t) | t<-Vec(1/sum(k=1, n, x^(k-1)/((2*k)!/k!), O(x^n)))]} \\ Andrew Howroyd, Nov 02 2019
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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