login
Decimal expansion of sum_{n>=1} n!/(3n)!.
4

%I #11 Oct 15 2014 20:59:39

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

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

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

%N Decimal expansion of sum_{n>=1} n!/(3n)!.

%e 0.1694610290320741286469267052989963331697124299377408004205540251006361...

%p evalf(sum(n!/(3*n)!, n=1..infinity),120) # _Vaclav Kotesovec_, Oct 15 2014

%t u = N[Sum[n!/(3 n)!, {n, 1, 200}], 120]

%t RealDigits[u] (* A248759 *)

%t N[HypergeometricPFQ[{1}, {4/3, 5/3}, 1/27]/6,120] (* _Vaclav Kotesovec_, Oct 15 2014 *)

%o (PARI) suminf(n=1, n!/(3*n)!) \\ _Michel Marcus_, Oct 15 2014

%Y Cf. A214869, A248696, A248760, A248761.

%K nonn,easy,cons

%O 0,2

%A _Clark Kimberling_, Oct 13 2014