A181044 The number of ways to compute the determinant of an n X n matrix using cofactor expansion.

1, 4, 384, 173946175488, 1592481597212922365761871004823571903636713118111555911680

Offset: 1

Author

Robert A. Beeler, Sep 30 2010

Keywords

• nonn

References

• Robert A. Beeler, How to Count: An Introduction to Combinatorics and Its Applications, Springer International Publishing, 2015. See Theorem 6.1.9 at p. 153.

Links

• Stefano Spezia, Table of n, a(n) for n = 1..6
• Robert A. Beeler, A Note on the number of ways to compute a determinant using cofactor expansion, Bull. Inst. Combin. Appl., 63 (2011), 36-38. [ResearchGate link]

Crossrefs

Cf. A363767.

Programs

Mathematica

a[1]=1; a[n_]:=2n a[n-1]^n; Array[a,5] (* Stefano Spezia, Jun 20 2023 *)

PARI

a(n) = if (n==1, 1, 2*n*a(n-1)^n); \\ Michel Marcus, Jun 21 2023

Formula

a(n) = 2*n*(a(n-1))^n.

a(n) = 2*2^n*2^(n*(n-1))*2^(n*(n-1)*(n-2))*...*2^(n*(n-1)*...*4*3)*n*(n-1)^n*(n-2)^(n*(n-1))*(n-3)^(n*(n-1)*(n-2))*...*2^(n*(n-1)*...*4*3).

From Robert A. Beeler, Oct 11 2010: (Start)

4^(n!*(e-2)) < a(n) < (2*e)^(n!*(e-2)).

a(n) ~ A363767^n!. (End)