A202688 Decimal expansion of Sum_{n>=0} (-1)^n / n!!.
2, 3, 8, 0, 3, 5, 1, 3, 6, 0, 5, 7, 6, 8, 0, 1, 4, 9, 1, 5, 7, 8, 2, 6, 0, 7, 6, 3, 9, 5, 0, 4, 8, 5, 3, 0, 3, 3, 0, 2, 9, 7, 4, 7, 5, 0, 8, 4, 9, 5, 5, 8, 1, 3, 8, 5, 0, 4, 3, 9, 8, 4, 3, 4, 7, 5, 8, 7, 9, 2, 2, 2, 7, 0, 3, 8, 1, 7, 6, 8, 1, 5, 1, 7, 3, 6, 7
Offset: 0
Examples
0.23803513605768014915782607639504...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
Programs
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Magma
SetDefaultRealField(RealField(112)); R:= RealField(); Exp(1/2)*(1 - Sqrt(Pi(R)/2)*Erf(1/Sqrt(2)) ); // G. C. Greubel, Mar 28 2019
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Maple
with(numtheory):Digits:=200:s:=evalf(sum(‘((-1)^(i+1))*doublefactorial(i)/i! ’,’i’=1..100)):print(s):
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Mathematica
RealDigits[N[Sum[((-1)^(n+1))/n!!,{n,0,100}],105]][[1]] RealDigits[Sqrt[E] - Sqrt[(E*Pi)/2]*Erf[1/Sqrt[2]], 10, 105][[1]] (* G. C. Greubel, Mar 28 2019 *) -
PARI
exp(.5) - sqrt(exp(1)*Pi/2)*(1-erfc(sqrt(.5))) \\ Charles R Greathouse IV, Nov 21 2016
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Sage
numerical_approx(exp(1/2)*(1 - sqrt(pi/2)*erf(1/sqrt(2))), digits=112) # G. C. Greubel, Mar 28 2019
Formula
Equals Sum_{n>=1} (-1)^(n+1)*n!! /n!.
Equals sqrt(e) - sqrt(e*Pi/2)*erf(1/sqrt(2)).
Extensions
Terms a(80) onward corrected by G. C. Greubel, Mar 28 2019
Name corrected by Thomas Ordowski, Oct 22 2024