login
Decimal expansion of Sum_{n>=0} (2n)!/(n!)^3 = Sum_{n>=0} C(2n,n)/n!.
1

%I #27 Mar 21 2021 12:04:37

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

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

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

%N Decimal expansion of Sum_{n>=0} (2n)!/(n!)^3 = Sum_{n>=0} C(2n,n)/n!.

%F Equals e^2 * BesselI(0,2) = e^2 * Sum_{n>=0} 1/n!^2.

%F Equals e^4 * Sum_{n>=0} (-1)^n * C(2n,n)/n!. - _Amiram Eldar_, Nov 06 2020

%e 16.843983681258...

%e Equals 1/1 + 2/1 + 24/8 + 720/216 + 40320/13824 + 3628800/1728000 + ...

%t RealDigits[E^2*BesselI[0, 2], 10, 100][[1]] (* _Amiram Eldar_, Nov 06 2020 *)

%o (PARI) exp(2)*besseli(0,2) \\ _Charles R Greathouse IV_, Feb 19 2014

%Y Cf. A000984, A070910.

%K nonn,cons

%O 2,2

%A _Richard R. Forberg_, Dec 31 2013

%E More terms from _Jon E. Schoenfield_, Mar 21 2021