A101800 a(n)= abs(det[A000166(i+j+1)]), i,j=0...n, is the absolute value of the Hankel determinant of order n+1 of the derangements numbers, cf. A000166.

0, 1, 16, 2160, 4644864, 220962816000, 126311423016960000, 97655159393202733056000000, 2873961139404949958783139840000000000, 5118723340142578530942677236206891171840000000000

Offset: 0

Author

Karol A. Penson, Dec 17 2004

Keywords

• nonn

Comments

a(n) = abs(product( (p!)^2,p=0..n )*(n+1)!*LaguerreL(n+1,0,1)), n=0,1..., where LaguerreL(n,lambda,x) are generalized Laguerre polynomial.

Crossrefs

Cf. A000166, A055209, A009940, A101799.

Programs

Mathematica

a[n_] := Table[Subfactorial[i+j+1], {i, 0, n}, {j, 0, n}] // Det // Abs;
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Aug 18 2024 *)

Formula

a(n) = abs(A055209(n)*A009940(n+1)). [corrected by Vaclav Kotesovec, Feb 25 2019]