cp's OEIS Frontend

A320637 Regular triangle read by rows: T(n,k) = Lcm_{m=k..n} d(n,k) where d(n,k) is the denominator of the unsigned Stirling1(n,k)*k!/n! for 0 <= k <= n.

%I A320637 #15 Jul 19 2022 08:08:19
%S A320637 1,1,1,1,2,1,1,6,1,1,1,12,12,2,1,1,60,12,4,1,1,1,60,180,8,6,2,1,1,420,
%T A320637 180,120,6,6,1,1,1,840,5040,240,240,6,4,2,1,1,2520,5040,15120,240,144,
%U A320637 4,12,1,1,1,2520,25200,30240,15120,288,240,24,3,2,1
%N A320637 Regular triangle read by rows: T(n,k) = Lcm_{m=k..n} d(n,k) where d(n,k) is the denominator of the unsigned Stirling1(n,k)*k!/n! for 0 <= k <= n.
%H A320637 Abdelmalek Bedhouche and Bakir Farhi, <a href="https://arxiv.org/abs/2207.07957">On some products taken over the prime numbers</a>, arXiv:2207.07957 [math.NT], 2022.
%H A320637 Bakir Farhi, <a href="https://arxiv.org/abs/1810.07560">On the derivatives of the integer-valued polynomials</a>, arXiv:1810.07560 [math.NT], 2018. See Table 1 c(n,k) p. 15.
%e A320637 Triangle begins:
%e A320637   1,
%e A320637   1, 1,
%e A320637   1, 2, 1,
%e A320637   1, 6, 1, 1,
%e A320637   1, 12, 12, 2, 1,
%e A320637   1, 60, 12, 4, 1, 1,
%e A320637   1, 60, 180, 8, 6, 2, 1,
%e A320637   1, 420, 180, 120, 6, 6, 1, 1,
%e A320637   ...
%o A320637 (PARI) d(n,k) = denominator(abs(stirling(n,k,1))*k!/n!);
%o A320637 T(n,k) = my(x = 1); for (m=k, n, x = lcm(x, d(m,k))); x;
%Y A320637 Cf. A000254, A003418, A141412.
%K A320637 nonn,tabl
%O A320637 0,5
%A A320637 _Michel Marcus_, Oct 18 2018
%E A320637 Corrected by _Michel Marcus_, Jul 19 2022