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 A362991 #22 Aug 09 2023 08:01:59
%S A362991 1,1,1,1,2,2,0,2,3,3,-2,2,9,12,12,0,-2,3,8,10,10,10,-10,-9,24,50,60,
%T A362991 60,0,20,-30,-8,50,90,105,105,-84,84,18,-96,0,150,245,280,280,0,-84,
%U A362991 126,-24,-90,18,147,224,252,252,2100,-2100,126,1344,-600,-870,343,1568,2268,2520,2520
%N A362991 Triangle read by rows. T(n, k) = lcm{1, 2, ..., n+1} * Sum_{j=0..n-k} (-1)^(n-k-j) * j! * Stirling2(n - k, j) / (j + k + 1).
%C A362991 A variant of the Akiyama-Tanigawa algorithm for the Bernoulli numbers A164555/ A027642.
%H A362991 Paolo Xausa, <a href="/A362991/b362991.txt">Table of n, a(n) for n = 0..11324</a> (rows 0..150 of the triangle, flattened)
%H A362991 M. Kaneko, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/KANEKO/AT-kaneko.html">The Akiyama-Tanigawa algorithm for Bernoulli numbers</a>, J. Integer Sequences, 3 (2000), #00.2.9.
%H A362991 D. Merlini, R. Sprugnoli, and M. C. Verri, <a href="https://www.emis.de/journals/INTEGERS/papers/f5/f5.Abstract.html">The Akiyama-Tanigawa Transformation</a>, Integers, 5 (1) (2005) #A05.
%H A362991 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.
%F A362991 T(n, 0) = lcm(1, 2, ..., n+1) * Bernoulli(n, 1).
%e A362991 Triangle T(n, k) starts:
%e A362991 [0] 1;
%e A362991 [1] 1, 1;
%e A362991 [2] 1, 2, 2;
%e A362991 [3] 0, 2, 3, 3;
%e A362991 [4] -2, 2, 9, 12, 12;
%e A362991 [5] 0, -2, 3, 8, 10, 10;
%e A362991 [6] 10, -10, -9, 24, 50, 60, 60;
%e A362991 [7] 0, 20, -30, -8, 50, 90, 105, 105;
%e A362991 [8] -84, 84, 18, -96, 0, 150, 245, 280, 280;
%e A362991 [9] 0, -84, 126, -24, -90, 18, 147, 224, 252, 252;
%p A362991 LCM := n -> ilcm(seq((1 + i), i = 0..n)):
%p A362991 T := (n, k) -> LCM(n)*add((-1)^(n - k - j)*j!*Stirling2(n - k, j)/(j + k + 1), j = 0..n - k):
%p A362991 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%t A362991 A362991row[n_]:=Table[LCM@@Range[n+1]Sum[(-1)^(n-k-j)j!StirlingS2[n-k,j]/(j+k+1),{j,0,n-k}],{k,0,n}];Array[A362991row,15,0] (* _Paolo Xausa_, Aug 09 2023 *)
%o A362991 (SageMath)
%o A362991 def A362991Triangle(size): # 'size' is the number of rows.
%o A362991 A, T, l = [], [], 1
%o A362991 for n in range(size):
%o A362991 A.append(Rational(1/(n + 1)))
%o A362991 for j in range(n, 0, -1):
%o A362991 A[j - 1] = j * (A[j - 1] - A[j])
%o A362991 l = lcm(l, n + 1)
%o A362991 T.append([a * l for a in A])
%o A362991 return T
%o A362991 A362991Triangle(10)
%Y A362991 Variant: A051714/A051715.
%Y A362991 Cf. A362994 (column 0), A002944 (main diagonal), A164555/A027642 (Bernoulli).
%K A362991 sign,tabl
%O A362991 0,5
%A A362991 _Peter Luschny_, May 16 2023