The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #20 Jul 03 2023 14:42:53
%S 0,1,-4,-12,32,80,-192,-448,1024,2304,-5120,-11264,24576,53248,
%T -114688,-245760,524288,1114112,-2359296,-4980736,10485760,22020096,
%U -46137344,-96468992,201326592,419430400,-872415232,-1811939328,3758096384,7784628224,-16106127360,-33285996544
%N Column 0 of triangle A118441, which is the matrix log of triangle A118435.
%H Stefano Spezia, <a href="/A118442/b118442.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-8,0,-16).
%F a(n) = (-1)^floor(n/2)*A001787(n).
%F G.f.: x*(1 - 4*x - 4*x^2)/(1 + 4*x^2)^2.
%F E.g.f.: x*(cos(2*x) - sin(2*x)). - _Stefano Spezia_, Jul 01 2023
%t LinearRecurrence[{0,-8,0,-16},{0,1,-4,-12},40] (* _Harvey P. Dale_, Dec 29 2014 *)
%o (PARI) {a(n)=polcoeff(x*(1 - 4*x - 4*x^2)/(1 + 4*x^2 +x*O(x^n))^2,n)}
%Y Cf. A118441 (triangle), A118443 (row sums); A118435, A001787.
%K sign,easy
%O 0,3
%A _Paul D. Hanna_, Apr 28 2006