A138706 a(n) is the sum of the terms in the continued fraction expansion of the absolute value of B_{2n}, the (2n)-th Bernoulli number.

1, 6, 30, 42, 30, 18, 37, 7, 28, 96, 559, 6210, 86617, 1425523, 27298263, 601580913, 15116315788, 429614643067, 13711655205344, 488332318973599, 19296579341940107, 841693047573684421, 40338071854059455479, 2115074863808199160579, 120866265222965259346062

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = A138703(2*n). - R. J. Mathar, Jul 20 2009

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 a(6) = 0 + 3 + 1 + 19 + 3 + 11 = 37.

Maple

A138704row := proc(n) local B; B := abs(bernoulli(2*n)) ; numtheory[cfrac](B, 20, 'quotients') ; end: A138706 := proc(n) add(c, c=A138704row(n)) ; end: seq(op(A138706(n)), n=0..30) ; # R. J. Mathar, Jul 20 2009

Mathematica

Table[Total[ContinuedFraction[Abs[BernoulliB[2n]]]], {n, 0, 25}] (* Harvey P. Dale, Feb 23 2012 *)

Prog

(PARI) a(n) = vecsum(contfrac(abs(bernfrac(2*n)))); \\ Jinyuan Wang, Aug 07 2021
(Python)
from sympy import continued_fraction, bernoulli
def A138706(n): return sum(continued_fraction(abs(bernoulli(n<<1)))) # Chai Wah Wu, Apr 14 2023

Crossrefs

Cf. A027641/A027642, A138703, A138704, A138705.

Sequence in context: A067879 A334900 A136375 * A027762 A002445 A151711

Adjacent sequences: A138703 A138704 A138705 * A138707 A138708 A138709

Keyword

nonn

Author

Leroy Quet, Mar 26 2008

Extensions

a(7)-a(22) from R. J. Mathar, Jul 20 2009

More terms from Jinyuan Wang, Aug 07 2021

Status

approved