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%I #18 Jan 14 2024 15:22:13
%S 1,6,30,420,630,13860,180180,5405400,4594590,96996900,1222160940,
%T 40156716600,6692786100,281097016200,1164544781400,72201776446800,
%U 2084826294901350,1895296631728500,222622144044300,1823275359722817000,575032998066426900,129519337183533297000
%N a(n) is the lcm of the denominators of the terms in the n-th row of M where M is the inverse of the matrix generated by the triangle A368846.
%C See A369134 for comments and formulas.
%t A368846[n_, k_] := If[k == 0, Boole[n == 0], (-1)^(n + k) 2 Binomial[2 k - 1, n] Binomial[2 n + 1, 2 k]];
%t LCM @@@ Denominator[MapIndexed[Take[#, First[#2]]&, Inverse[PadRight[Table[ A368846[n, k], {n, 0, 25}, {k, 0, n}]]]]] (* _Paolo Xausa_, Jan 14 2024 *)
%o (SageMath)
%o M = matrix(ZZ, 32, 32, A368846).inverse()
%o def A369135(n): return lcm(M[n][k].denominator() for k in range(n + 1))
%o print([A369135(n) for n in range(21)])
%Y Cf. A369134, A368846.
%K sign
%O 0,2
%A _Peter Luschny_, Jan 14 2024