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A335953
T(n, k) = numerator([x^k] b_n(x)), where b_n(x) = Sum_{k=0..n} binomial(n,k)*2^k* Bernoulli(k, 1/2)*x^(n-k). Triangle read by rows, for n >= 0 and 0 <= k <= n.
0
1, 0, 1, -1, 0, 1, 0, -1, 0, 1, 7, 0, -2, 0, 1, 0, 7, 0, -10, 0, 1, -31, 0, 7, 0, -5, 0, 1, 0, -31, 0, 49, 0, -7, 0, 1, 127, 0, -124, 0, 98, 0, -28, 0, 1, 0, 381, 0, -124, 0, 294, 0, -12, 0, 1, -2555, 0, 381, 0, -310, 0, 98, 0, -15, 0, 1
OFFSET
0,11
LINKS
Peter H. N. Luschny, An introduction to the Bernoulli function, arXiv:2009.06743 [math.HO], 2020.
EXAMPLE
[0] 1
[1] 0, 1
[2] -1, 0, 1
[3] 0, -1, 0, 1
[4] 7, 0, -2, 0, 1
[5] 0, 7, 0, -10, 0, 1
[6] -31, 0, 7, 0, -5, 0, 1
[7] 0, -31, 0, 49, 0, -7, 0, 1
[8] 127, 0, -124, 0, 98, 0, -28, 0, 1
[9] 0, 381, 0, -124, 0, 294, 0, -12, 0, 1
MAPLE
Bcn := n -> 2^n*bernoulli(n, 1/2):
Bcp := n -> add(binomial(n, k)*Bcn(k)*x^(n-k), k=0..n):
polycoeff := p -> seq(numer(coeff(p, x, k)), k = 0..degree(p, x)):
Trow := n -> polycoeff(Bcp(n)): seq(print(Trow(n)), n=0..9);
CROSSREFS
Cf. A285865 (denominators), A336454 (polynomial denominator), A336517, A001896, A001897.
Sequence in context: A222063 A156960 A287697 * A227958 A118858 A261167
KEYWORD
sign,tabl,frac
AUTHOR
Peter Luschny, Jul 25 2020
STATUS
approved