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%I #58 Jul 06 2023 21:08:34
%S 1,4,384,173946175488,
%T 1592481597212922365761871004823571903636713118111555911680
%N The number of ways to compute the determinant of an n X n matrix using cofactor expansion.
%D 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.
%H Stefano Spezia, <a href="/A181044/b181044.txt">Table of n, a(n) for n = 1..6</a>
%H Robert A. Beeler, <a href="https://www.researchgate.net/publication/265324328_A_note_on_the_number_of_ways_to_compute_a_determinant_using_cofactor_expansion">A Note on the number of ways to compute a determinant using cofactor expansion</a>, Bull. Inst. Combin. Appl., 63 (2011), 36-38. [ResearchGate link]
%F a(n) = 2*n*(a(n-1))^n.
%F 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).
%F From _Robert A. Beeler_, Oct 11 2010: (Start)
%F 4^(n!*(e-2)) < a(n) < (2*e)^(n!*(e-2)).
%F a(n) ~ A363767^n!. (End)
%t a[1]=1; a[n_]:=2n a[n-1]^n; Array[a,5] (* _Stefano Spezia_, Jun 20 2023 *)
%o (PARI) a(n) = if (n==1, 1, 2*n*a(n-1)^n); \\ _Michel Marcus_, Jun 21 2023
%Y Cf. A363767.
%K nonn
%O 1,2
%A _Robert A. Beeler_, Sep 30 2010
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