A228970 - OEIS

%I #25 Sep 15 2013 02:43:13

%S 5,7,7,85,17,85,341,341,341,341,455,91,65,91,455,5461,5461,5461,5461,

%T 5461,5461,4369,4369,21845,257,21845,4369,4369,9709,9709,1387,9709,

%U 9709,1387,9709,9709

%N 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.

%C GCD of rows (5, 7, 17, 341, 13, 5461 ...) are Zsigmondy numbers A064080. - _Paul Curtz_, Sep 13 2013

%D George Boros and Victor H. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press (2006), p. 100.

%H Jean-François Alcover, <a href="/A228970/b228970.txt">Table of n, a(n) for n = 2..105</a>

%e 6/5;

%e 5/7,        25/7;

%e 28/85,     70/17,  588/85;

%e 45/341, 1050/341, 4410/341, 3825/341;

%e ...

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

%Y Cf. A228969 (numerators), A064080 (Zsigmondy numbers).

%K frac,nonn,tabl

%O 2,1

%A _Jean-François Alcover_, Sep 10 2013