A130545 - OEIS

A130545

Numerators of 2*Sum_{k=1..n} 1/binomial(2*k,k), n >= 1.

1, 4, 43, 307, 463, 10201, 24121, 88453, 1503743, 28571327, 680271, 54761843, 156462429, 111170677, 245020174253, 7595625419003, 2531875141141, 17723125990639, 655755661678837, 655755661685297, 867289746102097

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OFFSET

1,2

COMMENTS

Partial sums (in lowest terms) for a series of (2/27)*(9+2*Pi*sqrt(3)).

The rationals r(n) = 2*Sum_{k=1..n} 1/binomial(2*k,k) tend, in the limit n->infinity, to (2/27)*(9 + 2*Pi*sqrt(3)), which is approximately 1.472799718.

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise (with a misprint).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

W. Lang, Rationals and limit.

FORMULA

a(n) = numerator(r(n)), n >= 1, with the rationals defined above.

EXAMPLE

Rationals r(n): 1, 4/3, 43/30, 307/210, 463/315, 10201/6930, 24121/16380, ....

MATHEMATICA

Numerator[Table[2*Sum[1/Binomial[2k, k], {k, n}], {n, 30}]] (* Harvey P. Dale, Jul 30 2015 *)

CROSSREFS