A167199 First column of A167196.
1, -2, 7, -36, 246, -2100, 21510, -257040, 3510360, -53933040, 920694600, -17288964000, 354169292400, -7859862410400, 187846741882800, -4810116703392000, 131382125482608000, -3812816394747360000, 117159925012065936000, -3800085546956707008000, 129743036125975752480000
Offset: 0
Programs
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Mathematica
CoefficientList[Series[2/(2+4*x+x^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)
Formula
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.
a(n) ~ n! * (-1)^n * (1+sqrt(2))/2 * (1+1/sqrt(2))^n. - Vaclav Kotesovec, Oct 08 2013
a(n) = ((sqrt(2) + 1)^(n+1) - (sqrt(2) - 1)^(n+1)) * n! * (-1)^n / 2^(n/2 + 1). - Enrique Navarrete, Aug 19 2025
Extensions
More terms from Amiram Eldar, May 05 2024
Comments