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.

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

Author

Peter Luschny, Jul 25 2020

Keywords

• sign
• tabl
• frac

Examples

			[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
		

Links

• Peter H. N. Luschny, An introduction to the Bernoulli function, arXiv:2009.06743 [math.HO], 2020.

Crossrefs

Cf. A285865 (denominators), A336454 (polynomial denominator), A336517, A001896, A001897.

Programs

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);