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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.
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%I #9 Aug 18 2024 14:10:46

%S 0,1,16,2160,4644864,220962816000,126311423016960000,

%T 97655159393202733056000000,2873961139404949958783139840000000000,

%U 5118723340142578530942677236206891171840000000000

%N 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.

%C 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.

%F a(n) = abs(A055209(n)*A009940(n+1)). [corrected by _Vaclav Kotesovec_, Feb 25 2019]

%t a[n_] := Table[Subfactorial[i+j+1], {i, 0, n}, {j, 0, n}] // Det // Abs;

%t Table[a[n], {n, 0, 9}] (* _Jean-François Alcover_, Aug 18 2024 *)

%Y Cf. A000166, A055209, A009940, A101799.

%K nonn

%O 0,3

%A _Karol A. Penson_, Dec 17 2004