A225112 Decimal expansion of integral of 1/binomial(2x,x) from x = 0 to infinity.

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

Offset: 1

Author

Michael Clausen, Apr 28 2013

Keywords

• nonn
• cons

Comments

The central binomial coefficient is extended to non-integer values via the Gamma function.

Examples

			1.221663899501...
		

Programs

Mathematica

NIntegrate[1/Binomial[2 t, t], {t, 0, Infinity}]

PARI

cbin(x)=exp(lngamma(2*x+1)-2*lngamma(x+1));
intnum(t=0,[oo,log(4)],1/cbin(t))
\\ Charles R Greathouse IV, Apr 30 2013

Formula

Integral(t = 0 .. infinity, 1/binomial(2t, t)).