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A362997 Triangle read by rows. T(n, k) = denominator([x^k] R(n, n, x)), where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).

%I A362997 #13 May 20 2023 08:22:19
%S A362997 1,2,1,6,3,1,12,3,4,1,60,15,20,5,1,20,5,20,15,6,1,140,35,140,105,42,7,
%T A362997 1,280,35,280,105,168,7,8,1,2520,315,280,315,504,7,72,9,1,2520,315,
%U A362997 280,315,504,35,360,45,10,1,27720,3465,3080,3465,5544,385,3960,495,110,11,1
%N A362997 Triangle read by rows. T(n, k) = denominator([x^k] R(n, n, x)), where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
%F A362997 T(n, k) = lcm(1, 2, ..., n+1) * A362996(n, k) / A362995(n, k).
%e A362997 Triangle T(n, k) starts:
%e A362997 [0]    1;
%e A362997 [1]    2,   1;
%e A362997 [2]    6,   3,   1;
%e A362997 [3]   12,   3,   4,   1;
%e A362997 [4]   60,  15,  20,   5,   1;
%e A362997 [5]   20,   5,  20,  15,   6,  1;
%e A362997 [6]  140,  35, 140, 105,  42,  7,   1;
%e A362997 [7]  280,  35, 280, 105, 168,  7,   8,  1;
%e A362997 [8] 2520, 315, 280, 315, 504,  7,  72,  9,  1;
%e A362997 [9] 2520, 315, 280, 315, 504, 35, 360, 45, 10, 1;
%o A362997 (SageMath)
%o A362997 def R(n, k, x):
%o A362997     return add((1 / (u + 1)) * add(x^j * binomial(u, j) * (j + 1)^n
%o A362997            for j in (0..u)) for u in (0..k))
%o A362997 def A362997row(n: int) -> list[int]:
%o A362997     return [r.denominator() for r in R(n, n, x).list()]
%o A362997 for n in (0..9): print(A362997row(n))
%Y A362997 Cf. A362996 (numerator), A002805 (column 0), A362995.
%K A362997 nonn,tabl,frac
%O A362997 0,2
%A A362997 _Peter Luschny_, May 13 2023