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A248181 Decimal expansion of Sum_{h >= 0} 1/binomial(h, floor(h/2)).

%I A248181 #17 Jul 01 2024 05:22:24
%S A248181 3,2,0,9,1,9,9,5,7,6,1,5,6,1,4,5,2,3,3,7,2,9,3,8,5,5,0,5,0,9,4,7,7,0,
%T A248181 4,8,8,1,8,9,3,7,7,4,9,8,7,2,8,4,9,3,7,1,7,0,4,6,5,8,9,9,5,6,9,2,5,4,
%U A248181 1,5,4,5,4,0,8,4,2,3,5,9,2,2,4,5,6,0
%N A248181 Decimal expansion of Sum_{h >= 0} 1/binomial(h, floor(h/2)).
%C A248181 Is this 2 + A248897? [_Bruno Berselli_, Mar 06 2015]. Yes, see Mathematica program below. - _Vaclav Kotesovec_, Jul 01 2024
%H A248181 Clark Kimberling, <a href="/A248181/b248181.txt">Table of n, a(n) for n = 0..1000</a>
%F A248181 Equals 2 + 2*Pi/3^(3/2). - _Vaclav Kotesovec_, Jul 01 2024
%e A248181 3.20919957615614523372938550509477048818...
%e A248181 Equals  1 + 1 + 1/2 + 1/3 + 1/6 + 1/10 + 1/20 + 1/35 + 1/70 + 1/126 + ...
%t A248181 r = N[Sum[1/Binomial[h, Floor[h/2]], {h, 0, 2000}], 200];
%t A248181 u = RealDigits[N[r, 200]][[1]]
%t A248181 (* or *)
%t A248181 Sum[1/Binomial[h, h/2], {h, 0, Infinity, 2}] + Sum[1/Binomial[h, (h-1)/2], {h, 1, Infinity, 2}] // Simplify // Expand (* _Vaclav Kotesovec_, Jul 01 2024 *)
%Y A248181 Cf. A248182.
%K A248181 nonn,easy,cons
%O A248181 0,1
%A A248181 _Clark Kimberling_, Oct 04 2014