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

Author

Leroy Quet, Mar 26 2008

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

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

More terms from Jinyuan Wang, Aug 07 2021