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A248676 Decimal expansion of r = sum_{n >= 0} floor(n/3)!/n!.

%I A248676 #9 Oct 17 2014 05:25:21
%S A248676 2,7,1,9,9,0,9,2,6,5,4,9,0,8,5,3,8,3,4,2,1,3,2,2,2,8,6,5,2,2,4,5,2,5,
%T A248676 2,1,1,9,3,3,1,0,0,7,6,0,4,8,4,7,1,6,7,2,7,5,0,8,5,8,8,5,5,8,9,5,9,7,
%U A248676 4,1,7,4,6,6,1,0,2,9,5,5,8,4,9,5,0,1
%N A248676 Decimal expansion of r = sum_{n >= 0} floor(n/3)!/n!.
%H A248676 Clark Kimberling, <a href="/A248676/b248676.txt">Table of n, a(n) for n = 1..1000</a>
%F A248676 r = sum_{n >= 0} p(3,n)*n!/(3*n + 2)!, where p(k,n) is defined at A248664.
%e A248676 r = 2.71990926549085383421322286522452521...
%p A248676 evalf(sum(floor(n/3)!/n!, n=0..infinity),120); # _Vaclav Kotesovec_, Oct 17 2014
%t A248676 x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
%t A248676 RealDigits[x][[1]]  (* A248675 *)
%t A248676 x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
%t A248676 RealDigits[x][[1]]  (* A248676 *)
%t A248676 x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
%t A248676 RealDigits[x][[1]]  (* A248677 *)
%Y A248676 Cf. A248675, A248677, A248664.
%K A248676 nonn,easy,cons
%O A248676 1,1
%A A248676 _Clark Kimberling_, Oct 11 2014