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A202367 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). 11

%I

%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 Brian Diaz, <a href="https://arxiv.org/abs/2010.13645">Asymptotics on a class of Legendre formulas</a>, arXiv:2010.13645 [math.NT], 2020.

%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. A053657.

%K nonn

%O 1,2

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 18 2011

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Last modified June 13 22:11 EDT 2021. Contains 345010 sequences. (Running on oeis4.)