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).

1, 6, 360, 45360, 5443200, 359251200, 5884534656000, 35307207936000, 144053408378880000, 1034591578977116160000, 3414152210624483328000000, 471153005066178699264000000, 15434972445968014187888640000000, 92609834675808085127331840000000, 161141112335906068121557401600000000

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Dec 18 2011

Keywords

• nonn

Comments

See comment in A175669.

Links

• Maiyu Diaz, Asymptotics on a class of Legendre formulas, arXiv:2010.13645 [math.NT], 2020.
• Wataru Takeda, On the Bhargava factorial of polynomial maps, arXiv:2304.02946 [math.NT], 2023. Mentions this sequence.

Crossrefs

Cf. A007814, A053657, A175669.

Formula

Conjecture: a(n) = Product_{primes p} p^(Sum_{k>=0} floor((n-1)/(ceiling((p-1)/2)*p^k))).

If the conjecture is true, then, for n >= 0, A007814(a(n+1)) = A007814(n!) + n.