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A288873
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Numerators of scaled Bernoulli numbers 4^n*B(n), with B(n) = A027641(n)/A027642(n).
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0
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1, -2, 8, 0, -128, 0, 2048, 0, -32768, 0, 2621440, 0, -5796528128, 0, 939524096, 0, -7767448354816, 0, 1507258642989056, 0, -95993412418797568, 0, 7516375836686024704, 0, -33265288504730187726848, 0, 19259875741830735724544, 0, -855664510723636131971203072, 0, 4966694343692730467779807805440
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OFFSET
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0,2
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COMMENTS
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The denominators seem to be given in A141459.
See A285863 for comments on B(d;n) = d^n*B(n), for n >= 0, with e.g.f. d*x/(exp(d*x) - 1).
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LINKS
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FORMULA
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a(n) = numerator(r(n)), with the rationals r(n) = 4^n*A027641(n)/A027642(n), n >= 0.
E.g.f. of {r(n)}_{n>=0}: 4*x/(exp(4*x) - 1).
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EXAMPLE
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The rationals r(n) begin: 1, -2, 8/3, 0, -128/15, 0, 2048/21, 0, -32768/15, 0, 2621440/33, 0, -5796528128/1365, 0, 939524096/3, 0, -7767448354816/255, 0, 1507258642989056/399, 0, -95993412418797568/165, ...
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MAPLE
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seq(numer(4^n*bernoulli(n)), n=0..28); # Peter Luschny, Jul 17 2017
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MATHEMATICA
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PROG
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(PARI) a(n) = numerator(4^n*bernfrac(n)); \\ Michel Marcus, Jul 06 2017
(Python)
from sympy import bernoulli
def a(n): return (4**n * bernoulli(n)).numerator()
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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STATUS
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approved
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