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
Examples
6/5; 5/7, 25/7; 28/85, 70/17, 588/85; 45/341, 1050/341, 4410/341, 3825/341; ...
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
Programs
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Mathematica
Table[(2^(2*k) - 1)/(2^(2*n) - 1)* Binomial[2*n, 2*k], {n, 2, 9}, {k, 1, n-1}] // Flatten // Denominator
Comments