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URL: https://oeis.org/A394198

⇱ A394198 - OEIS

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A394198
Total number of linear intervals in the weak order on the Coxeter group D_n.
1
1248, 17216, 269568, 4732416, 92160000, 1972887552, 46068203520, 1165619036160, 31774337925120, 928516276224000, 28959369005629440, 960261079538073600, 33735701275921612800, 1251834624646683033600, 48927351154151522304000, 2009139126253980431155200, 86482397103403554570240000
OFFSET
4,1
COMMENTS
An interval is linear of height k if it is isomorphic to the total order on k+1 elements.
See A394193 for the number of linear intervals of a given height.
PROG
(SageMath)
def a(n):
s = 1 + n/2
for k in range(2, n):
s += 2 * (n-k+1)/(k+1)
if k == 3:
s += 1/2
return s * factorial(n) * 2^(n-1)
print([a(n) for n in range(4, 20)])
CROSSREFS
Cf. A002866, A344216 (type A), A394191 (type B), A394193.
Sequence in context: A184500 A234212 A047629 * A221012 A233167 A266037
KEYWORD
nonn
AUTHOR
Ludovic Schwob, Mar 12 2026
STATUS
approved