A375693 Number of multiset permutations of {{1}^n, {2}^n, ..., {n}^n} with no fixed n-tuple {j}^n.

1, 0, 5, 1622, 62924817, 623302086965044, 2670169511426774520697375, 7363615066099523741730150062678073534, 18165723898797467057177720588121375861340650728031233, 53130688704554689391452744667655289291011354800478739192999936981375688

Offset: 0

Author

Alois P. Heinz, Aug 24 2024

Keywords

• nonn

Examples

			a(2) = 5: 1212, 1221, 2112, 2121, 2211.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..26

Crossrefs

Main diagonal of A375694.

Cf. A034841, A059841, A306241, A375778.

Programs

Maple

a:= n-> add((-1)^(n-j)*binomial(n, j)*(n*j)!/n!^j, j=0..n):
seq(a(n), n=0..10);

Formula

a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(n*j)!/n!^j.

a(n) mod 2 = 1 - (n mod 2) = A059841(n).