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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.
2
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: A028316 A377656 A019163 * A266712 A021177 A091662
KEYWORD
frac,nonn,tabl
AUTHOR
STATUS
approved