%I #14 Nov 19 2015 10:04:14

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

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

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

%N Decimal expansion of sum_{n >= 1} (2n)!/(1!*2!*...*n!).

%C Let t(n) = (2n)!/(1!*2!*...*n!). Then t(n) is an integer for n = 1..5, and max{t(n), n >= 1} = t(4) = 140... . It appears that t(n) < 10^(-6) for n > 9.

%e 338.9492801098942429745072350488697681125523042506474491612493021261451367444...

%p evalf(sum((2*n)!/product(k!, k=1..n), n=1..infinity), 120); # _Vaclav Kotesovec_, Oct 19 2014

%t u = N[Sum[(2 n)!/Product[k!, {k, 1, n}], {n, 1, 300}], 120]

%t RealDigits[u] (* A248696 *)

%t NSum[(2 n)!/BarnesG[n+2], {n, 1, Infinity}, WorkingPrecision -> 103] // RealDigits // First (* _Jean-François Alcover_, Nov 19 2015 *)

%o (PARI) suminf(n=1, (2*n)!/prod(k=1, n, k!)) \\ _Michel Marcus_, Oct 19 2014

%Y Cf. A214869, A248695.

%K nonn,easy,cons

%O 3,1

%A _Clark Kimberling_, Oct 13 2014

%E More digits from _Jean-François Alcover_, Nov 19 2015