login
Sums of the cubes of the descent set statistics for permutations on n elements.
3

%I #19 Dec 20 2020 12:38:57

%S 1,1,2,18,360,14460,994680,109021500,17815754880,4147063256448,

%T 1323985303267200,562636176102554400,310405397451855552000,

%U 217731000904433587359360,190749857434239995742090240,205540893695782384696324368000,268793206446238988670401236992000

%N Sums of the cubes of the descent set statistics for permutations on n elements.

%H R. Ehrenborg and A. Happ, <a href="https://arxiv.org/abs/1709.00778">On the powers of the descent set statistic</a>, arXiv:1709.00778 [math.CO], 2017.

%F a(n) = Sum_{j=0..ceiling(2^(n-1))-1} A060351(n,j)^3. - _Alois P. Heinz_, Sep 15 2020

%e For n=4, we have a(4) = 1^3 + 3^3 + 5^5 + 3^3 + 3^3 + 5^3 + 3^3 + 1^3 = 360.

%Y Cf. A060350, A291903, A060351.

%Y Column k=3 of A334622.

%K nonn

%O 0,3

%A _Richard Ehrenborg_, Sep 05 2017

%E a(0)=1 prepended by _Alois P. Heinz_, Sep 09 2020