A375778 Number of multiset permutations of {{1}^n, {2}^n, ..., {n}^n} with no fixed points.

1, 0, 1, 56, 748521, 2671644472544, 4165949769769961828425, 4198063809561374304863859278045664, 3792196761630663647644729491214828673313675120817, 4066336002770373278819438293126282402268149361469069425278228336256

Offset: 0

Author

Alois P. Heinz, Aug 27 2024

Keywords

• nonn

Examples

			a(0) = 1: the empty permutation.
a(2) = 1: 2211.
a(3) = 56: 222333111, 223133112, 223133121, 223133211, 223313112, 223313121, 223313211, 223331112, 223331121, 223331211, 232133112, 232133121, 232133211, 232313112, 232313121, 232313211, 232331112, 232331121, 232331211, 233113122, 233113212, 233113221, 233131122, 233131212, 233131221, 233311122, 233311212, 233311221, 322133112, 322133121, 322133211, 322313112, 322313121, 322313211, 322331112, 322331121, 322331211, 323113122, 323113212, 323113221, 323131122, 323131212, 323131221, 323311122, 323311212, 323311221, 332113122, 332113212, 332113221, 332131122, 332131212, 332131221, 332311122, 332311212, 332311221, 333111222.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..27

Crossrefs

Main diagonal of A372307.

Cf. A059841, A375693.

Programs

Maple

a:= n-> (-1)^n*int(exp(-x)*orthopoly[L](n, x)^n, x=0..infinity):
seq(a(n), n=0..10);

Mathematica

a[n_] := (-1)^n*Integrate[Exp[-x]*LaguerreL[n, x]^n, {x, 0, Infinity}];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Sep 02 2024, after Alois P. Heinz *)

Formula

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