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

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, 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, 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

Offset: 0

Author

Fred Daniel Kline, Mar 11 2013

Keywords

• nonn
• cons

Comments

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

Examples

			0.5922965364693265756604150545390626872846166122169...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• 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.
• Eric Weisstein's World of Mathematics, Erf

Programs

Maple

evalf(1/2*exp(1/4)*Pi^(1/2)*erf(1/2),120) # Vaclav Kotesovec, Oct 16 2014

Mathematica

NSum[n!/(2 n)!, {n, 1, Infinity}, WorkingPrecision -> 105]
RealDigits[1/2*E^(1/4)*Sqrt[Pi]*Erf[1/2], 10, 105][[1]] (* Jean-François Alcover, Feb 20 2014 *)

PARI

/* needs GP version >= 2.6 */
N=200;
default(realprecision, N+10);
s=suminf(n=1,n!/(2*n)!);
digits( floor( 10^N*s ), 10 )
/* Joerg Arndt, Mar 11 2013 */