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A335953
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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.
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0
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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
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OFFSET
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0,11
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LINKS
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EXAMPLE
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[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
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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