A377135 Number of maximal chains in the poset of n-ary words of length n ordered by B covers A iff A_i <= B_i for 1 <= i <= n.

1, 1, 2, 90, 369600, 305540235000, 88832646059788350720, 14007180988362844601443040716800, 1707750599894443404262670865631874246246400000, 217425846656446788579638892849417587480505167467321080630000000

Offset

0,3

Comments

Terms are divisible by n for n > 0.

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = Product_{i=0..n-2} binomial((n-1)*(n-i),n-1).

a(n) = (n*(n-1))!/(n-1)!^n for n>=1, a(0)=1. - Alois P. Heinz, Nov 27 2024

Example

For a(2) = (1,1) < (2,1) < (2,2), (1,1) < (1,2) < (2,2).
For n = 3 one chain is (1,1,1) < (1,2,1) < (1,2,2) < (1,2,3) < (1,3,3) < (2,3,3) < (3,3,3).

Maple

a:= n-> (t-> (n*t)!/t!^n)(max(n-1, 0)):
seq(a(n), n=0..10);  # Alois P. Heinz, Nov 27 2024

Mathematica

a[n_]:=Product[Binomial[(n-1)*(n-i), n-1], {i, 0, n-2}]; Array[a, 10, 0] (* Stefano Spezia, Nov 27 2024 *)

Prog

(PARI)
a(n) = {if(n<1, 1, (n*(n-1))!/(n-1)!^n)}

Crossrefs

Cf. A000312, A034841, A300385, A378382.

Sequence in context: A157064 A058527 A342329 * A306760 A306964 A138583

Adjacent sequences: A377132 A377133 A377134 * A377136 A377137 A377138

Keyword

nonn,easy

Author

John Tyler Rascoe, Nov 26 2024

Status

approved