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%I #16 Oct 01 2022 06:08:26
%S 1,-2,-12,-40,-112,-288,-704,-1664,-3840,-8704,-19456,-43008,-94208,
%T -204800,-442368,-950272,-2031616,-4325376,-9175040,-19398656,
%U -40894464,-85983232,-180355072,-377487360,-788529152,-1644167168,-3422552064,-7113539584,-14763950080
%N a(n) = (1-2n)*2^n.
%C Hankel transform of abs(A002420) (which is 2*0^n - binomial(2n,n)/(2n-1)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F G.f.: (1-6x)/(1-2x)^2;
%F a(n) = Sum_{k=0..n} A121314(n,k)*(-1)^k*2^(3n-2k). - _Philippe Deléham_, Oct 31 2008
%F From _Amiram Eldar_, Oct 01 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1 - arcsinh(1)/sqrt(2).
%F Sum_{n>=0} (-1)^n/a(n) = 1 + arctan(1/sqrt(2))/sqrt(2). (End)
%t a[n_] := (1-2n)*2^n; Array[a, 40, 0] (* _Amiram Eldar_, Oct 01 2022 *)
%Y Cf. A002420, A118417, A121314.
%K easy,sign
%O 0,2
%A _Paul Barry_, Jul 26 2008
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