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%I #21 Nov 10 2020 08:21:08
%S 1,0,-1,2,5,-8,3,8,141,-204,11,-4,-11,-30,99,1836,164997,-224532,2403,
%T -126,-39,14,-5,-14,-267,-738,351,-1134,-28431,-538002,9537507,
%U 891167508,361226647845,-471103550820,1127461923,-11787930,-675783,34992,-1377,-432,-927
%N Determinant of the n X n Hankel matrix whose entries are s_2 (i+j), 0 <= i, j < n, where s_2 is the sum of the base-2 bits.
%C Hankel transform of A000120.
%H Alois P. Heinz, <a href="/A056886/b056886.txt">Table of n, a(n) for n = 0..350</a>
%e a(2) = -1 because det [[0,1],[1,1]] = -1.
%p with(LinearAlgebra):
%p wt:= proc(n) local m, t; m:=n; t:=0;
%p while m>0 do t:= t+irem(m, 2, 'm') od; t
%p end:
%p a:= n-> Determinant(Matrix(n, (i, j)-> wt(i+j-2))):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, May 25 2013
%t a[n_] := Det[Array[DigitCount[#1 + #2 - 2, 2, 1]&, {n, n}]]; a[0] = 1;
%t a /@ Range[0, 40] (* _Jean-François Alcover_, Nov 10 2020 *)
%o (PARI) {a(n) = if( n<0, 0, matdet( matrix( n, n, i, j, 2*i + 2*j - 4 - valuation( (2*i + 2*j - 4)!, 2))))} /* _Michael Somos_, Feb 08 2011 */
%K sign,look
%O 0,4
%A _Jeffrey Shallit_, Sep 04 2000
%E a(0)=1 added by _Michael Somos_, Feb 08 2011
%E More terms from _Alois P. Heinz_, May 25 2013
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