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A285866
a(n) = numerator((-2)^n*Sum_{k=0..n} binomial(n,k) * Bernoulli(k, 1/2)).
2
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
OFFSET
0,2
COMMENTS
Previous name: Numerators of alternating row sums of the rational triangle B2 = A285864/A285865.
The denominators are given in A141459.
FORMULA
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).
MAPLE
a := n -> numer((-2)^n*add(binomial(n, k)*bernoulli(k, 1/2), k=0..n)):
seq(a(n), n=0..31); # Peter Luschny, Jul 24 2020
MATHEMATICA
a[n_] := (-2)^n Sum[Binomial[n, k] BernoulliB[k, 1/2], {k, 0, n}] // Numerator;
Table[a[n], {n, 0, 31}] (* Peter Luschny, Jul 24 2020 *)
PROG
(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
CROSSREFS
KEYWORD
sign,easy,frac
AUTHOR
Wolfdieter Lang, May 03 2017
EXTENSIONS
More terms from Indranil Ghosh, May 06 2017
New name by Peter Luschny, Jul 24 2020
STATUS
approved