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%I #12 May 05 2024 01:47:37
%S 1,-2,7,-36,246,-2100,21510,-257040,3510360,-53933040,920694600,
%T -17288964000,354169292400,-7859862410400,187846741882800,
%U -4810116703392000,131382125482608000,-3812816394747360000,117159925012065936000,-3800085546956707008000,129743036125975752480000
%N First column of A167196.
%C Limiting ratio 2+n*a(n-1)/a(n) converges to A002193.
%F Conjecture: E.g.f.: 2/(2+4*x+x^2) = G(0)/(1+x) where G(k) = 1 - x/((1+x) - x*(1+x)/(x - (1+x)*2/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Dec 28 2012.
%F a(n) ~ n! * (-1)^n * (1+sqrt(2))/2 * (1+1/sqrt(2))^n. - _Vaclav Kotesovec_, Oct 08 2013
%t CoefficientList[Series[2/(2+4*x+x^2), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 08 2013 *)
%Y Cf. A167196, A002193.
%K sign
%O 0,2
%A _Mats Granvik_, Oct 30 2009
%E More terms from _Amiram Eldar_, May 05 2024