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

1,2

Comments

See comment in A175669.

Links

Table of n, a(n) for n=1..15.

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.

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.

Crossrefs

Cf. A007814, A053657, A175669.

Sequence in context: A367519 A002684 A036281 * A262179 A064350 A069945

Adjacent sequences: A202364 A202365 A202366 * A202368 A202369 A202370

Keyword

nonn

Author

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

Status

approved