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A202688 Decimal expansion of Sum_{n>=0} (-1)^(n+1) / 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 (list; constant; graph; refs; listen; history; text; internal format)
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€™, 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: A048979 A088332 A131959 * A021046 A138180 A079585

Adjacent sequences:  A202685 A202686 A202687 * A202689 A202690 A202691

KEYWORD

nonn,cons

AUTHOR

Michel Lagneau, Dec 24 2011

EXTENSIONS

Terms a(80) onward corrected by G. C. Greubel, Mar 28 2019

STATUS

approved

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Last modified June 6 17:01 EDT 2020. Contains 334829 sequences. (Running on oeis4.)