A138704 Irregular array read by rows: row n contains the continued fraction terms (in order) for the absolute value of B_{2n}, the (2n)th Bernoulli number.

1, 0, 6, 0, 30, 0, 42, 0, 30, 0, 13, 5, 0, 3, 1, 19, 3, 11, 1, 6, 7, 10, 1, 5, 1, 2, 2, 54, 1, 33, 1, 2, 3, 2, 529, 8, 20, 2, 6192, 8, 8, 2, 86580, 3, 1, 19, 3, 11, 1425517, 6, 27298231, 14, 1, 2, 1, 14, 601580873, 1, 9, 15, 2, 7, 6, 15116315767, 10, 1, 5, 1, 2, 2, 429614643061, 6

Offset: 0

Author

Leroy Quet, Mar 26 2008

Keywords

• nonn
• tabf

Comments

The number of terms in row n is A138705(n).

Examples

			The 12th Bernoulli number is -691/2730. Now 691/2730 has the continued fraction 0 + 1/(3 + 1/(1 + 1/(19 + 1/(3 + 1/11)))). So row 6 is (0,3,1,19,3,11).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..2884

Crossrefs

Cf. A138701, A138705, A138706, A000367, A002445.

Programs

Maple

A138704row := proc(n) local B; B := abs(bernoulli(2*n)) ; numtheory[cfrac](B,20,'quotients') ; end: seq(op(A138704row(n)),n=0..20) ; # R. J. Mathar, Jul 20 2009

Mathematica

Array[ContinuedFraction@ Abs@ BernoulliB[2 #] &, 18, 0] // Flatten (* Michael De Vlieger, Oct 18 2017 *)

Extensions

More terms from R. J. Mathar, Jul 20 2009