cp's OEIS Frontend

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.

%I A377135 #37 Nov 29 2024 17:59:25
%S A377135 1,1,2,90,369600,305540235000,88832646059788350720,
%T A377135 14007180988362844601443040716800,
%U A377135 1707750599894443404262670865631874246246400000,217425846656446788579638892849417587480505167467321080630000000
%N 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.
%C A377135 Terms are divisible by n for n > 0.
%F A377135 a(n) = Product_{i=0..n-2} binomial((n-1)*(n-i),n-1).
%F A377135 a(n) = (n*(n-1))!/(n-1)!^n for n>=1, a(0)=1. - _Alois P. Heinz_, Nov 27 2024
%e A377135 For a(2) = (1,1) < (2,1) < (2,2), (1,1) < (1,2) < (2,2).
%e A377135 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).
%p A377135 a:= n-> (t-> (n*t)!/t!^n)(max(n-1, 0)):
%p A377135 seq(a(n), n=0..10);  # _Alois P. Heinz_, Nov 27 2024
%t A377135 a[n_]:=Product[Binomial[(n-1)*(n-i),n-1],{i,0,n-2}]; Array[a,10,0] (* _Stefano Spezia_, Nov 27 2024 *)
%o A377135 (PARI)
%o A377135 a(n) = {if(n<1,1,(n*(n-1))!/(n-1)!^n)}
%Y A377135 Cf. A000312, A034841, A300385, A378382.
%K A377135 nonn,easy
%O A377135 0,3
%A A377135 _John Tyler Rascoe_, Nov 26 2024