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A138706
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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.
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4
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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Table[Total[ContinuedFraction[Abs[BernoulliB[2n]]]], {n, 0, 25}] (* Harvey P. Dale, Feb 23 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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