A228969 Triangle of numerators 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.

6, 5, 25, 28, 70, 588, 45, 1050, 4410, 3825, 22, 165, 924, 2805, 7502, 91, 5005, 63063, 255255, 341341, 124215, 24, 1820, 168168, 12870, 2730728, 496860, 131064, 17, 1700, 6188, 413270, 1657942, 402220, 1856740, 371365

Offset: 2

Author

Jean-François Alcover, Sep 10 2013

Keywords

• frac
• nonn
• tabl

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, Cambridge University Press (2006), p. 100.

Links

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

Crossrefs

Cf. A228970 (denominators).

Programs

Mathematica

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