%I #41 Feb 11 2024 11:22:43

%S 5,9,2,2,9,6,5,3,6,4,6,9,3,2,6,5,7,5,6,6,0,4,1,5,0,5,4,5,3,9,0,6,2,6,

%T 8,7,2,8,4,6,1,6,6,1,2,2,1,6,9,8,7,1,0,3,7,7,5,6,8,5,8,3,6,5,3,2,0,3,

%U 6,7,9,6,1,6,6,5,0,7,5,5,7,0,2,7,2,4,4,3,5,1,5,7,5,0,7,6,1,0,4,2,5,5,3,5,3

%N Decimal expansion of Sum_{n >= 1} n!/(2*n)!.

%C Equivalent to: 1/2 e^(1/4) Pi^(1/2) erf(1/2) where erf(1/2) is error function.

%H G. C. Greubel, <a href="/A214869/b214869.txt">Table of n, a(n) for n = 0..5000</a>

%H J.-P. Allouche and T. Baruchel, <a href="http://arxiv.org/abs/1408.2206">Variations on an error sum function for the convergents of some powers of e</a>, arXiv preprint arXiv:1408.2206 [math.NT], 2014.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Erf.html">Erf</a>

%e 0.5922965364693265756604150545390626872846166122169...

%p evalf(1/2*exp(1/4)*Pi^(1/2)*erf(1/2),120) # _Vaclav Kotesovec_, Oct 16 2014

%t NSum[n!/(2 n)!, {n, 1, Infinity}, WorkingPrecision -> 105]

%t RealDigits[1/2*E^(1/4)*Sqrt[Pi]*Erf[1/2], 10, 105][[1]] (* _Jean-François Alcover_, Feb 20 2014 *)

%o (PARI) /* needs GP version >= 2.6 */

%o N=200;

%o default(realprecision, N+10);

%o s=suminf(n=1,n!/(2*n)!);

%o digits( floor( 10^N*s ), 10 )

%o /* _Joerg Arndt_, Mar 11 2013 */

%K nonn,cons

%O 0,1

%A _Fred Daniel Kline_, Mar 11 2013