OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
FORMULA
Equals Sum_{n>=1} (-1)^(n+1)*n!! /n!.
Equals sqrt(e) - sqrt(e*Pi/2)*erf(1/sqrt(2)).
EXAMPLE
0.23803513605768014915782607639504...
MAPLE
with(numtheory):Digits:=200:s:=evalf(sum(ā((-1)^(i+1))*doublefactorial(i)/i! ā, āiā=1..100)):print(s):
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 *)
PROG
(PARI) exp(.5) - sqrt(exp(1)*Pi/2)*(1-erfc(sqrt(.5))) \\ Charles R Greathouse IV, Nov 21 2016
(Magma) SetDefaultRealField(RealField(112)); R:= RealField(); Exp(1/2)*(1 - Sqrt(Pi(R)/2)*Erf(1/Sqrt(2)) ); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx(exp(1/2)*(1 - sqrt(pi/2)*erf(1/sqrt(2))), digits=112) # G. C. Greubel, Mar 28 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Michel Lagneau, Dec 24 2011
EXTENSIONS
Terms a(80) onward corrected by G. C. Greubel, Mar 28 2019
Name corrected by Thomas Ordowski, Oct 22 2024
STATUS
approved