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A285866
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a(n) = numerator((-2)^n*Sum_{k=0..n} binomial(n,k) * Bernoulli(k, 1/2)).
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2
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1, -2, 11, -6, 127, -10, 221, -14, 367, -18, -1895, -22, 1447237, -26, -57253, -30, 118526399, -34, -5749677193, -38, 91546283957, -42, -1792042789427, -46, 1982765468376757, -50, -286994504449237, -54, 3187598676787485443, -58, -4625594554880206360895, -62
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OFFSET
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0,2
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COMMENTS
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Previous name: Numerators of alternating row sums of the rational triangle B2 = A285864/A285865.
The denominators are given in A141459.
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LINKS
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FORMULA
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a(n) = numerator(Sum_{m=0..n} (-1)^m*A285864(n, m)/A285865(n, m)), n >= 0, where the rational triangle is B2(n, m) = binomial(m, m)*2^(n-m)*B(n-m), with the Bernoulli numbers B(k) = A027641(k)/A027642(k).
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MAPLE
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a := n -> numer((-2)^n*add(binomial(n, k)*bernoulli(k, 1/2), k=0..n)):
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MATHEMATICA
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a[n_] := (-2)^n Sum[Binomial[n, k] BernoulliB[k, 1/2], {k, 0, n}] // Numerator;
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PROG
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(SageMath) # uses [gen_bernoulli_number from A157811]
print([numerator((-1)^n*gen_bernoulli_number(n, 2)) for n in range(33)]) # Peter Luschny, Mar 26 2021
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CROSSREFS
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KEYWORD
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sign,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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