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

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, 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, 1, 5, 4, 5, 4, 0, 8, 4, 2, 3, 5, 9, 2, 2, 4, 5, 6, 0

Offset: 0

Author

Clark Kimberling, Oct 04 2014

Keywords

• nonn
• easy
• cons

Comments

Is this 2 + A248897? [Bruno Berselli, Mar 06 2015]. Yes, see Mathematica program below. - Vaclav Kotesovec, Jul 01 2024

Examples

			3.20919957615614523372938550509477048818...
Equals  1 + 1 + 1/2 + 1/3 + 1/6 + 1/10 + 1/20 + 1/35 + 1/70 + 1/126 + ...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A248182.

Programs

Mathematica

r = N[Sum[1/Binomial[h, Floor[h/2]], {h, 0, 2000}], 200];
u = RealDigits[N[r, 200]][[1]]
(* or *)
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 *)

Formula

Equals 2 + 2*Pi/3^(3/2). - Vaclav Kotesovec, Jul 01 2024