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%I #30 Apr 07 2023 09:27:49
%S 1,6,360,45360,5443200,359251200,5884534656000,35307207936000,
%T 144053408378880000,1034591578977116160000,3414152210624483328000000,
%U 471153005066178699264000000,15434972445968014187888640000000,92609834675808085127331840000000,161141112335906068121557401600000000
%N LCM of denominators of the coefficients of polynomials Q^(2)_m(n) defined by the recursion Q^(2)_0(n)=1; for m >= 1, Q^(2)_m(n) = Sum_{i=1..n} i^2*Q^(2)_(m-1)(i).
%C See comment in A175669.
%H Maiyu Diaz, <a href="https://arxiv.org/abs/2010.13645">Asymptotics on a class of Legendre formulas</a>, arXiv:2010.13645 [math.NT], 2020.
%H Wataru Takeda, <a href="https://arxiv.org/abs/2304.02946">On the Bhargava factorial of polynomial maps</a>, arXiv:2304.02946 [math.NT], 2023. Mentions this sequence.
%F Conjecture: a(n) = Product_{primes p} p^(Sum_{k>=0} floor((n-1)/(ceiling((p-1)/2)*p^k))).
%F If the conjecture is true, then, for n >= 0, A007814(a(n+1)) = A007814(n!) + n.
%Y Cf. A007814, A053657, A175669.
%K nonn
%O 1,2
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 18 2011
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