A138704 - OEIS

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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

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OFFSET

0,3

COMMENTS

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

LINKS

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

EXAMPLE

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).

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 *)

CROSSREFS

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

Sequence in context: A062254 A028849 A287470 * A005396 A056462 A249869

Adjacent sequences: A138701 A138702 A138703 * A138705 A138706 A138707

KEYWORD

nonn,tabf

AUTHOR

Leroy Quet, Mar 26 2008

EXTENSIONS

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

STATUS

approved