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%I #11 Feb 08 2022 21:58:20
%S 1,2,2,2,4,12,34,86,200,440,934,1938,3964,8036,16202,32558,65296,
%T 130800,261838,523946,1048196,2096732,4193842,8388102,16776664,
%U 33553832,67108214,134217026,268434700,536870100,1073740954,2147482718
%N A007318 * [1, 1, -1, 1, 1, 1, ...].
%F Binomial transform of [1, 1, -1, 1, 1, 1, ...].
%F From _R. J. Mathar_, Jul 31 2008: (Start)
%F O.g.f.: x(1-3x+x^2+3x^3)/((1-x)^3*(1-2x)).
%F a(n) = 4n - 2 - 2*A000217(n) + 2^(n-1). (End)
%F a(n) = 2^n - n(n-1) (if offset is 0). - _Emeric Deutsch_, Aug 09 2008
%e a(6) = 12 = (1, 5, 10, 10, 5, 1) dot (1, 1, -1, 1, 1, 1) = (1 + 5 - 10 + 10, + 5, + 1).
%p a:=proc(n) options operator, arrow: 2^n-n*(n-1) end proc: seq(a(n),n=0..32); # _Emeric Deutsch_, Aug 09 2008
%t Table[2^n-n(n-1),{n,0,3*4!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 25 2010 *)
%K nonn
%O 1,2
%A _Gary W. Adamson_, Jul 15 2008
%E More terms from _Emeric Deutsch_, Aug 09 2008
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