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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A067879 A334900 A136375 * A027762 A002445 A151711
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)