cp's OEIS Frontend

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.

%I A335953 #8 Dec 16 2020 19:15:48
%S A335953 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,
%T A335953 -31,0,49,0,-7,0,1,127,0,-124,0,98,0,-28,0,1,0,381,0,-124,0,294,0,-12,
%U A335953 0,1,-2555,0,381,0,-310,0,98,0,-15,0,1
%N 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.
%H A335953 Peter H. N. Luschny, <a href="https://arxiv.org/abs/2009.06743">An introduction to the Bernoulli function</a>, arXiv:2009.06743 [math.HO], 2020.
%e A335953 [0]   1
%e A335953 [1]   0,   1
%e A335953 [2]  -1,   0,    1
%e A335953 [3]   0,  -1,    0,    1
%e A335953 [4]   7,   0,   -2,    0,  1
%e A335953 [5]   0,   7,    0,  -10,  0,   1
%e A335953 [6] -31,   0,    7,    0, -5,   0,   1
%e A335953 [7]   0, -31,    0,   49,  0,  -7,   0,   1
%e A335953 [8] 127,   0, -124,    0, 98,   0, -28,   0, 1
%e A335953 [9]   0, 381,    0, -124,  0, 294,   0, -12, 0, 1
%p A335953 Bcn := n -> 2^n*bernoulli(n, 1/2):
%p A335953 Bcp := n -> add(binomial(n, k)*Bcn(k)*x^(n-k), k=0..n):
%p A335953 polycoeff := p -> seq(numer(coeff(p, x, k)), k = 0..degree(p, x)):
%p A335953 Trow := n -> polycoeff(Bcp(n)): seq(print(Trow(n)), n=0..9);
%Y A335953 Cf. A285865 (denominators), A336454 (polynomial denominator), A336517, A001896, A001897.
%K A335953 sign,tabl,frac
%O A335953 0,11
%A A335953 _Peter Luschny_, Jul 25 2020