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

2,1

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

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 // Numerator

Crossrefs

Cf. A228970 (denominators).

Sequence in context: A082384 A248265 A267284 * A256961 A371253 A267743

Adjacent sequences: A228966 A228967 A228968 * A228970 A228971 A228972

Keyword

frac,nonn,tabl

Author

Jean-François Alcover, Sep 10 2013

Status

approved