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Decimal expansion of sum_{n>=1} 1/(n*binomial(5*n,n)).
0

%I #7 May 17 2013 09:47:59

%S 2,1,1,8,9,9,3,7,9,4,7,7,9,8,8,0,4,0,6,2,0,1,4,7,6,8,4,2,2,7,9,2,2,2,

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

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

%N Decimal expansion of sum_{n>=1} 1/(n*binomial(5*n,n)).

%C Equals Integral_{x>0}((4*x)/((1 + x)*(1 + 4*x + 10*x^2 + 10*x^3 + 5*x^4 + x^5))).

%D George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 60.

%e 0.211899379477988040620147684227922292577929674144068015360748567774676347301...

%t (1/5)*HypergeometricPFQ[{1, 1, 5/4, 3/2, 7/4}, {6/5, 7/5, 8/5, 9/5}, 256/3125] // RealDigits[#, 10, 105]& // First

%Y Cf. A073010, A210453.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, May 17 2013