cp's OEIS Frontend

A130306 Degree of the scheme of n X n complex matrices that square to zero.

%I A130306 #17 Dec 04 2018 17:26:36
%S A130306 1,2,2,12,28,440,2456,98448,1327632,134302752,4398726432,
%T A130306 1116577758912,89104889764288,56558827752672128,11021135122877392256,
%U A130306 17451895365397015875840,8316834448188073547563264,32799202036840274283669160448,38271513084756431661704424923648
%N A130306 Degree of the scheme of n X n complex matrices that square to zero.
%H A130306 Alois P. Heinz, <a href="/A130306/b130306.txt">Table of n, a(n) for n = 0..100</a>
%H A130306 A. Knutson and P. Zinn-Justin, <a href="http://arXiv.org/abs/math.AG/0503224">A scheme related to the Brauer loop model</a>, Adv. in Math. 214 (2007), 40-77.
%F A130306 a(2n) = 2^n * det(binomial(2i+2j+1,2i)), 0<=i,j<=n-1; a(2n+1) = 2^(n+1) * det(binomial(2i+2j+3,2i+1)), 0<=i,j<=n-1.
%e A130306 In size 1, the scheme {x^2=0} is of degree 2. in size 2, the scheme of matrices {{m11,m12},{m21,m22}} that square to zero is generically reduced and the corresponding reduced scheme is given by the equations m11+m22=0 and m11^2+m12 m21=0, hence also of degree 2.
%t A130306 a[1] = 2; a[n_] := If[EvenQ[n], 2^(n/2) Det[Table[Binomial[2i + 2j + 1, 2i], {i, 0, n/2-1}, {j, 0, n/2-1}]], 2^((n-1)/2+1) Det[Table[Binomial[2i + 2j + 3, 2i + 1], {i, 0, (n-1)/2-1}, {j, 0, (n-1)/2-1}]]];
%t A130306 Array[a, 12] (* _Jean-François Alcover_, Dec 04 2018 *)
%Y A130306 Cf. A130294.
%K A130306 nonn
%O A130306 0,2
%A A130306 _Paul Zinn-Justin_, Aug 06 2007
%E A130306 More terms from _Alois P. Heinz_, Dec 04 2018