A228970 Triangle of denominators of the coefficients t(n,k) in the formula B(2n) = -sum_{k=1..n-1} t(n,k)*B(2k)*B(2n-2k), where the B() are the even-indexed Bernoulli numbers.

5, 7, 7, 85, 17, 85, 341, 341, 341, 341, 455, 91, 65, 91, 455, 5461, 5461, 5461, 5461, 5461, 5461, 4369, 4369, 21845, 257, 21845, 4369, 4369, 9709, 9709, 1387, 9709, 9709, 1387, 9709, 9709

Offset

2,1

Comments

GCD of rows (5, 7, 17, 341, 13, 5461 ...) are Zsigmondy numbers A064080. - Paul Curtz, Sep 13 2013

References

George Boros and Victor H. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press (2006), p. 100.

Links

Jean-François Alcover, Table of n, a(n) for n = 2..105

Example

6/5;
5/7,        25/7;
28/85,     70/17,  588/85;
45/341, 1050/341, 4410/341, 3825/341;
...

Mathematica

Table[(2^(2*k) - 1)/(2^(2*n) - 1)* Binomial[2*n, 2*k], {n, 2, 9}, {k, 1, n-1}] // Flatten // Denominator

Crossrefs

Cf. A228969 (numerators), A064080 (Zsigmondy numbers).

Sequence in context: A126992 A028316 A019163 * A266712 A021177 A091662

Adjacent sequences: A228967 A228968 A228969 * A228971 A228972 A228973

Keyword

frac,nonn,tabl

Author

Jean-François Alcover, Sep 10 2013

Status

approved