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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A267743 A298155

Adjacent sequences:  A228966 A228967 A228968 * A228970 A228971 A228972

KEYWORD

frac,nonn,tabl

AUTHOR

Jean-François Alcover, Sep 10 2013

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)