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A202688 Decimal expansion of Sum_{n>=0} (-1)^n / n!!.

%I A202688 #22 Oct 22 2024 03:24:48
%S A202688 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,
%T A202688 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,
%U A202688 9,2,2,2,7,0,3,8,1,7,6,8,1,5,1,7,3,6,7
%N A202688 Decimal expansion of Sum_{n>=0} (-1)^n / n!!.
%H A202688 G. C. Greubel, <a href="/A202688/b202688.txt">Table of n, a(n) for n = 0..10000</a>
%F A202688 Equals Sum_{n>=1} (-1)^(n+1)*n!! /n!.
%F A202688 Equals sqrt(e) - sqrt(e*Pi/2)*erf(1/sqrt(2)).
%e A202688 0.23803513605768014915782607639504...
%p A202688 with(numtheory):Digits:=200:s:=evalf(sum(‘((-1)^(i+1))*doublefactorial(i)/i! ’,’i’=1..100)):print(s):
%t A202688 RealDigits[N[Sum[((-1)^(n+1))/n!!,{n,0,100}],105]][[1]]
%t A202688 RealDigits[Sqrt[E] - Sqrt[(E*Pi)/2]*Erf[1/Sqrt[2]], 10, 105][[1]] (* _G. C. Greubel_, Mar 28 2019 *)
%o A202688 (PARI) exp(.5) - sqrt(exp(1)*Pi/2)*(1-erfc(sqrt(.5))) \\ _Charles R Greathouse IV_, Nov 21 2016
%o A202688 (Magma) SetDefaultRealField(RealField(112)); R:= RealField(); Exp(1/2)*(1 - Sqrt(Pi(R)/2)*Erf(1/Sqrt(2)) ); // _G. C. Greubel_, Mar 28 2019
%o A202688 (Sage) numerical_approx(exp(1/2)*(1 - sqrt(pi/2)*erf(1/sqrt(2))), digits=112) # _G. C. Greubel_, Mar 28 2019
%Y A202688 Cf. A006882 (n!!), A143280 (m(2)).
%K A202688 nonn,cons
%O A202688 0,1
%A A202688 _Michel Lagneau_, Dec 24 2011
%E A202688 Terms a(80) onward corrected by _G. C. Greubel_, Mar 28 2019
%E A202688 Name corrected by _Thomas Ordowski_, Oct 22 2024