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%I #14 Feb 14 2019 07:45:26
%S 1,1,2,1,2,6,1,2,3,1,1,2,12,3,30,1,2,24,9,20,1,1,2,48,54,80,10,42,1,2,
%T 96,324,8640,200,105,1,1,2,192,1944,3840,36000,525,35,30,1,2,384,
%U 11664,1244160,720000,756000,3675,168,1
%N Triangle read by rows, a generalization of the Bernoulli numbers, the denominators for n>=0 and 0<=k<=n.
%C See comments in A292900.
%H S. Fukuhara, N. Kawazumi and Y. Kuno, <a href="https://arxiv.org/abs/1505.04840">Generalized Kronecker formula for Bernoulli numbers and self-intersections of curves on a surface</a>, arXiv:1505.04840 [math.NT], 2015.
%H L. Kronecker, <a href="http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002158752">Ueber die Bernoullischen Zahlen</a>, J. Reine Angew. Math. 94 (1883), 268-269.
%e Triangle starts:
%e [0], 1
%e [1], 1, 2
%e [2], 1, 2, 6
%e [3], 1, 2, 3, 1
%e [4], 1, 2, 12, 3, 30
%e [5], 1, 2, 24, 9, 20, 1
%e [6], 1, 2, 48, 54, 80, 10, 42
%e [7], 1, 2, 96, 324, 8640, 200, 105, 1
%e [8], 1, 2, 192, 1944, 3840, 36000, 525, 35, 30
%e [9], 1, 2, 384, 11664, 1244160, 720000, 756000, 3675, 168, 1
%p # Function B(n,k) in A292900.
%p for n from 0 to 9 do seq(denom(B(n, k)), k=0..n) od;
%t B[0, 0] = 1; B[n_, k_] := Sum[(-1)^(j-n)/(j+1) Binomial[k+1, j+1] Sum[i^n (j-i+1)^(k-n), {i, 0, j}], {j, 0, k}]; Table[B[n, k] // Denominator, {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 14 2019, from Maple *)
%Y Cf. A292900 (numerators), T(n, n) = A027642(n).
%K nonn,tabl,frac
%O 0,3
%A _Peter Luschny_, Oct 01 2017
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