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A248675 Decimal expansion of r = sum_{n >= 0} floor(n/2)!/n!.

%I A248675 #18 Oct 17 2014 05:24:32
%S A248675 2,7,7,6,8,8,9,6,0,9,4,0,7,9,7,9,7,2,6,9,8,1,2,4,5,1,6,3,6,1,7,1,8,8,
%T A248675 0,6,1,8,5,3,8,4,9,8,3,6,6,5,0,9,6,1,3,1,1,3,2,7,0,5,7,5,0,9,5,9,6,1,
%U A248675 1,0,3,8,8,4,9,9,5,2,2,6,7,1,0,8,1,7
%N A248675 Decimal expansion of r = sum_{n >= 0} floor(n/2)!/n!.
%H A248675 Clark Kimberling, <a href="/A248675/b248675.txt">Table of n, a(n) for n = 1..1000</a>
%F A248675 r = sum_{n >= 0} p(2,n)*n!/(2*n + 1)!, where p(k,n) is defined at A248664.
%e A248675 r = 2.7768896094079797269812451636...
%p A248675 evalf(sum(floor(n/2)!/n!, n=0..infinity),120); # _Vaclav Kotesovec_, Oct 17 2014
%t A248675 x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
%t A248675 RealDigits[x][[1]]  (* A248675 *)
%t A248675 x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
%t A248675 RealDigits[x][[1]]  (* A248676 *)
%t A248675 x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
%t A248675 RealDigits[x][[1]]  (* A248677 *)
%Y A248675 Cf. A248676, A248677, A248664.
%K A248675 nonn,easy,cons
%O A248675 1,1
%A A248675 _Clark Kimberling_, Oct 11 2014