A394193 - OEIS

A394193

Irregular triangle read by rows: T(n,k) is the number of linear intervals of height k in the weak order on D_n (0 <= k <= n-1).

192, 384, 384, 288, 1920, 4800, 5120, 3840, 1536, 23040, 69120, 76800, 57600, 27648, 15360, 322560, 1128960, 1290240, 967680, 516096, 322560, 184320, 5160960, 20643840, 24084480, 18063360, 10321920, 6881280, 4423680, 2580480, 92897280, 418037760, 495452160, 371589120, 222953472, 154828800, 106168320, 69672960, 41287680

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OFFSET

4,1

COMMENTS

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

LINKS

Table of n, a(n) for n=4..42.

FORMULA

Row sums give A394198.

EXAMPLE

Triangle begins:

192, 384, 384, 288;

1920, 4800, 5120, 3840, 1536;

23040, 69120, 76800, 57600, 27648, 15360;

PROG

(SageMath)

def T(n, k):

if k < 0 or k >= n:

return 0

nW = factorial(n) * 2^(n-1)

if k == 0:

return nW

if k == 1:

return nW * n/2

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

if k == 3:

s += 1/2

return s * nW

CROSSREFS

Cf. A002866, A391308 (type A), A394190 (type B), A394198.

Sequence in context: A234135 A030632 A189987 * A229361 A232940 A254854

Adjacent sequences: A394190 A394191 A394192 * A394194 A394195 A394196

KEYWORD

nonn,tabf

AUTHOR

Ludovic Schwob, Mar 12 2026

STATUS

approved