A154242 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)).

1, 3, 45, 1890, 56700, 748440, 10216206000, 8756748000, 2841962760000, 24946749107280000, 8232427205402400000, 103279541304139200000, 3101484625363300176000000, 1431454442475369312000000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

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)))).

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A012494 A012780 A072503 * A331710 A283698 A163002

Adjacent sequences: A154239 A154240 A154241 * A154243 A154244 A154245

Keyword

nonn,frac

Author

Roger L. Bagula, Jan 05 2009

Status

approved