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A202688
Decimal expansion of Sum_{n>=0} (-1)^n / n!!.
1
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
0,1
LINKS
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€™, ā€™iā€™=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
Cf. A006882 (n!!), A143280 (m(2)).
Sequence in context: A088332 A357064 A131959 * A021046 A138180 A345093
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