A130547 - OEIS

A130547

Numerators of 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3), n >= 1.

1, 2, 23, 167, 253, 5581, 13201, 48413, 823063, 15638407, 1117033, 89921239, 256917887, 60848977, 134111147453, 4157445588203, 1385815197541, 9700706385439, 358926136286437, 358926136292897, 474708760905697

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Denominators are given by A130548.

The partial sums (in lowest terms) r(n) = 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3) tend, for n->infinity, to 4*Pi*sqrt(3)/9, which is approximately 2.418399153.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..21.

W. Lang, Rationals and limit.

FORMULA

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

MATHEMATICA

Table[6*(Sum[1/Binomial[2k, k], {k, n}]-1/3), {n, 30}]//Numerator (* Harvey P. Dale, Jul 07 2021 *)

CROSSREFS

Sequence in context: A356828 A220239 A189977 * A352355 A200846 A198851

Adjacent sequences: A130544 A130545 A130546 * A130548 A130549 A130550

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Jul 13 2007

STATUS

approved