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

0,2

Comments

Limiting ratio 2+n*a(n-1)/a(n) converges to A002193.

Links

Table of n, a(n) for n=0..20.

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

Mathematica

CoefficientList[Series[2/(2+4*x+x^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)

Crossrefs

Cf. A167196, A002193.

Sequence in context: A029768 A180271 A380081 * A007889 A125033 A034430

Adjacent sequences: A167196 A167197 A167198 * A167200 A167201 A167202

Keyword

sign

Author

Mats Granvik, Oct 30 2009

Extensions

More terms from Amiram Eldar, May 05 2024

Status

approved