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A210685 a(1)=-1, a(2)=2, thereafter a(n) = (1/(2n))*((7n-22)a(n-1)+2(2n-1)a(n-2)).

%I A210685 #14 May 19 2024 08:40:54
%S A210685 -1,2,-2,2,-1,2,2,8,22,68,212,678,2207,7298,24458,82928,284066,981884,
%T A210685 3421316,12007556,42416486,150718772,538421588,1932856592,6969847484,
%U A210685 25237057112,91729488352,334589415278,1224445617887,4494622119426,16545704494682,61071167108960,225982053183050
%N A210685 a(1)=-1, a(2)=2, thereafter a(n) = (1/(2n))*((7n-22)a(n-1)+2(2n-1)a(n-2)).
%H A210685 Liu Yanpei, <a href="https://doi.org/10.1016/0095-8956(84)90018-2">On the number of rooted c-nets</a>, J. Combin. Theory, B 36 (1984), 118-123. See the sequence R_n.
%F A210685 A000287(n) = (-1)^n*2 + a(n-1).
%p A210685 R:=proc(n) option remember; if n=1 then -1 elif n=2 then 2 else
%p A210685 (1/(2*n))*((7*n-22)*R(n-1)+2*(2*n-1)*R(n-2)); fi; end;
%p A210685 [seq(R(n),n=1..40)];
%t A210685 a[n_] := a[n] = Which[n == 1, -1, n == 2, 2, True, (1/(2*n))*((7*n-22)*a[n-1]+2*(2*n-1)*a[n-2])]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Mar 06 2014, after Maple *)
%Y A210685 Cf. A000287.
%K A210685 sign
%O A210685 1,2
%A A210685 _N. J. A. Sloane_, Mar 28 2012