%I #7 Mar 17 2026 18:35:01

%S 1248,17216,269568,4732416,92160000,1972887552,46068203520,

%T 1165619036160,31774337925120,928516276224000,28959369005629440,

%U 960261079538073600,33735701275921612800,1251834624646683033600,48927351154151522304000,2009139126253980431155200,86482397103403554570240000

%N Total number of linear intervals in the weak order on the Coxeter group D_n.

%C An interval is linear of height k if it is isomorphic to the total order on k+1 elements.

%C See A394193 for the number of linear intervals of a given height.

%o (SageMath)

%o def a(n):

%o s = 1 + n/2

%o for k in range(2, n):

%o s += 2 * (n-k+1)/(k+1)

%o if k == 3:

%o s += 1/2

%o return s * factorial(n) * 2^(n-1)

%o print([a(n) for n in range(4, 20)])

%Y Cf. A002866, A344216 (type A), A394191 (type B), A394193.

%K nonn

%O 4,1

%A _Ludovic Schwob_, Mar 12 2026