A154243 Numerators 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)).

2, -1, 1, -1, -1, 1, 23, -23, 157, 97051, -1614583, -331691, 1418383997, -5720927, -1868325937, 1207461869239, 118209298450003, -3069893653, -14303719087308533, 65108016166881997, -310766859240153209819

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = numerator([x^n]*(1/Sum_{k>=1} x^(k-1)/((2*k)!/k!)).

a(n) = numerator([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[ Numerator[SeriesCoefficient[Series[p[x], {x, 0, 30}], n]], {n, 0, 30}]

Prog

(PARI) seq(n)={[numerator(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: A256671 A327156 A114171 * A326698 A299432 A252911

Adjacent sequences: A154240 A154241 A154242 * A154244 A154245 A154246

Keyword

sign,frac

Author

Roger L. Bagula, Jan 05 2009

Status

approved