cp's OEIS Frontend

A214869 Decimal expansion of Sum_{n >= 1} n!/(2*n)!.

%I A214869 #42 Feb 16 2025 08:33:18
%S A214869 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 A214869 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 A214869 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 A214869 Decimal expansion of Sum_{n >= 1} n!/(2*n)!.
%C A214869 Equivalent to: 1/2 e^(1/4) Pi^(1/2) erf(1/2) where erf(1/2) is error function.
%H A214869 G. C. Greubel, <a href="/A214869/b214869.txt">Table of n, a(n) for n = 0..5000</a>
%H A214869 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 A214869 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Erf.html">Erf</a>
%e A214869 0.5922965364693265756604150545390626872846166122169...
%p A214869 evalf(1/2*exp(1/4)*Pi^(1/2)*erf(1/2),120) # _Vaclav Kotesovec_, Oct 16 2014
%t A214869 NSum[n!/(2 n)!, {n, 1, Infinity}, WorkingPrecision -> 105]
%t A214869 RealDigits[1/2*E^(1/4)*Sqrt[Pi]*Erf[1/2], 10, 105][[1]] (* _Jean-François Alcover_, Feb 20 2014 *)
%o A214869 (PARI)  /* needs GP version >= 2.6 */
%o A214869 N=200;
%o A214869 default(realprecision, N+10);
%o A214869 s=suminf(n=1,n!/(2*n)!);
%o A214869 digits( floor( 10^N*s ), 10 )
%o A214869 /* _Joerg Arndt_, Mar 11 2013 */
%K A214869 nonn,cons
%O A214869 0,1
%A A214869 _Fred Daniel Kline_, Mar 11 2013