%I #15 Mar 14 2023 13:32:29

%S 0,6,30,42,30,14,231,4,322,125580,6,11,802,1124805,2,3,8,78,41496,9,

%T 77,6930,9,83,34362,4,322,125580,6,15,870,2,3,15,1557,9291398,

%U 172660144297410,11,802,1124805,6,4,13,171,885780,6

%N Irregular array read by rows, where n-th row gives denominators of the Egyptian fraction expansion, derived using the greedy algorithm, for the absolute value of the fractional part of the (2n)th Bernoulli number.

%e Triangle begins:

%e 0,

%e 6,

%e 30,

%e 42,

%e 30,

%e 14, 231

%e 4, 322, 125580

%e ...

%e The 10th Bernoulli number is 5/66. The largest unit fraction <= 5/66 is 1/14. Now 5/66 - 1/14 is 1/231, which is itself a unit fraction. So the Egyptian fraction representation of 5/66 is 1/14 + 1/231. Therefore row 5 of this array is (14,231).

%Y Cf. A000367, A002445.

%Y Row sums: A151711. - _N. J. A. Sloane_, Jun 07 2009

%K more,nonn,tabf

%O 0,2

%A _Leroy Quet_, Mar 29 2008

%E Row 6 from _N. J. A. Sloane_, Jun 07 2009

%E Better definition and more terms from _T. D. Noe_, Jun 07 2009