This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342322 #14 Apr 10 2021 20:07:54
%S A342322 1,0,1,0,-1,2,0,0,-1,1,0,1,1,-9,6,0,0,1,1,-4,2,0,-1,-1,6,6,-15,6,0,0,
%T A342322 -2,-2,5,5,-9,3,0,3,3,-17,-17,25,25,-35,10,0,0,3,3,-7,-7,7,7,-8,2,0,
%U A342322 -5,-5,28,28,-38,-38,28,28,-27,6,0,0,-10,-10,23,23,-21,-21,12,12,-10,2
%N A342322 T(n, k) = A064538(n)*[x^k] p(n, x) where p(n, x) = 1 + Sum_{k = 0..n-1} binomial[n, k]*p(k, 1)* ((x - 1)^(n - k) - 1) / (n - k + 1) for n >= 1 and p(0, x) = 1. Triangle read by rows, for 0 <= k <= n.
%F A342322 (Sum_{k = 0..n} T(n, k)) / A064538(n) = Bernoulli(n, 1).
%e A342322 p(n, x) = (Sum_{k = 0..n} T(n, k) x^k) / A064538(n).
%e A342322 [n] T(n, k) A064538(n)
%e A342322 ---------------------------------------------------
%e A342322 [0] 1, [ 1]
%e A342322 [1] 0, 1, [ 2]
%e A342322 [2] 0, -1, 2, [ 6]
%e A342322 [3] 0, 0, -1, 1, [ 4]
%e A342322 [4] 0, 1, 1, -9, 6, [30]
%e A342322 [5] 0, 0, 1, 1, -4, 2, [12]
%e A342322 [6] 0, -1, -1, 6, 6, -15, 6, [42]
%e A342322 [7] 0, 0, -2, -2, 5, 5, -9, 3, [24]
%e A342322 [8] 0, 3, 3, -17, -17, 25, 25, -35, 10, [90]
%e A342322 [9] 0, 0, 3, 3, -7, -7, 7, 7, -8, 2. [20]
%p A342322 CoeffList := p -> [op(PolynomialTools:-CoefficientList(factor(p), x))]:
%p A342322 p := n -> add(binomial(n+1,k+1)*bernoulli(n-k, 1)*(x-1)^k, k=0..n)/(n+1):
%p A342322 seq(print(denom(p(n))*CoeffList(p(n))), n=0..9);
%t A342322 (* Uses the function A064538. *)
%t A342322 p[n_, x_] := p[n, x] = If[n == 0, 1, 1 +
%t A342322 Sum[Binomial[n, k] p[k, 1] ((x - 1)^(n - k) - 1) / (n - k + 1), {k, 0, n-1}]];
%t A342322 Table[A064538[n] CoefficientList[p[n, x], x][[k+1]], {n, 0, 9}, {k, 0, n}] // Flatten
%Y A342322 Cf. A064538.
%K A342322 sign,frac,tabl
%O A342322 0,6
%A A342322 _Peter Luschny_, Mar 09 2021