A291902 Sums of the cubes of the descent set statistics for permutations on n elements.

1, 1, 2, 18, 360, 14460, 994680, 109021500, 17815754880, 4147063256448, 1323985303267200, 562636176102554400, 310405397451855552000, 217731000904433587359360, 190749857434239995742090240, 205540893695782384696324368000, 268793206446238988670401236992000

Offset

0,3

Links

Table of n, a(n) for n=0..16.

R. Ehrenborg and A. Happ, On the powers of the descent set statistic, arXiv:1709.00778 [math.CO], 2017.

Formula

a(n) = Sum_{j=0..ceiling(2^(n-1))-1} A060351(n,j)^3. - Alois P. Heinz, Sep 15 2020

Example

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

Crossrefs

Cf. A060350, A291903, A060351.

Column k=3 of A334622.

Sequence in context: A349881 A181536 A132911 * A336217 A226837 A152684

Adjacent sequences: A291899 A291900 A291901 * A291903 A291904 A291905

Keyword

nonn

Author

Richard Ehrenborg, Sep 05 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 09 2020

Status

approved