A380082 Number of Boolean intervals of rank 2 in the weak order of the Coxeter group of type C_n, for n >= 2

0, 12, 288, 5760, 115200, 2419200, 54190080, 1300561920, 33443020800, 919683072000, 26977370112000, 841693947494400, 27852417898905600, 974834626461696000, 35993893900124160000, 1398619877261967360000, 57063690992288268288000, 2439472789920323469312000, 109058783549379166863360000

Offset

2,2

Comments

Proof in Adenbaum et al., 2024 (full reference below).

Links

Table of n, a(n) for n=2..20.

Ben Adenbaum, Jennifer Elder, Pamela E. Harris, and J. Carlos Martínez Mori, Boolean intervals in the weak Bruhat order of a finite Coxeter group, arXiv:2403.07989 [math.CO], 2024.

Formula

a(n) = n! * binomial(n - 1, 2) * 2^(n - 2).

Prog

(PARI) a(n) = n! * binomial(n-1, 2) * 2^(n-2); \\ Michel Marcus, Feb 19 2025

Crossrefs

Sequence in context: A267670 A159827 A192191 * A145448 A321938 A001164

Adjacent sequences: A380079 A380080 A380081 * A380084 A380085 A380086

Keyword

nonn

Author

J. Carlos Martínez Mori, Feb 18 2025

Extensions

More terms from Michel Marcus, Feb 19 2025

Status

approved