# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a214869 Showing 1-1 of 1 %I A214869 #41 Feb 11 2024 11:22:43 %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, Table of n, a(n) for n = 0..5000 %H A214869 J.-P. Allouche and T. Baruchel, Variations on an error sum function for the convergents of some powers of e, arXiv preprint arXiv:1408.2206 [math.NT], 2014. %H A214869 Eric Weisstein's World of Mathematics, Erf %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE