cp's OEIS Frontend

A248677 Decimal expansion of r = sum_{n >= 0} floor(n/4)!/n!.

%I A248677 #8 Oct 17 2014 05:25:12
%S A248677 2,7,1,8,3,0,9,6,9,7,7,0,7,2,4,5,6,1,8,3,3,0,4,0,8,2,7,6,3,6,1,8,7,3,
%T A248677 4,7,9,6,2,8,7,6,1,1,1,3,3,9,4,8,9,6,3,4,3,2,0,6,4,4,2,4,2,6,1,7,4,1,
%U A248677 3,1,3,5,4,3,9,1,2,8,2,4,3,8,1,9,6,1
%N A248677 Decimal expansion of r = sum_{n >= 0} floor(n/4)!/n!.
%H A248677 Clark Kimberling, <a href="/A248677/b248677.txt">Table of n, a(n) for n = 1..1000</a>
%F A248677 r = sum_{n >= 0} p(4,n)*n!/(4*n + 3)!, where p(k,n) is defined at A248664.
%e A248677 r = 2.718309697707245618330408276361873...
%p A248677 evalf(sum(floor(n/4)!/n!, n=0..infinity),120); # _Vaclav Kotesovec_, Oct 17 2014
%t A248677 x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
%t A248677 RealDigits[x][[1]]  (* A248675 *)
%t A248677 x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
%t A248677 RealDigits[x][[1]]  (* A248676 *)
%t A248677 x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
%t A248677 RealDigits[x][[1]]  (* A248677 *)
%Y A248677 Cf. A248675, A248676, A248664.
%K A248677 nonn,easy,cons
%O A248677 1,1
%A A248677 _Clark Kimberling_, Oct 11 2014