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%I #11 Sep 08 2022 08:45:55
%S 1,0,1,5,4,84,296,2680,19776,182336,1812352,19963008,239490560,
%T 3113532928,43589096448,653837290496,10461394714624,177843714539520,
%U 3201186851815424,60822550206644224,1216451004083601408,25545471085864681472,562000363888782868480,12926008369442532360192,310224200866619627405312,7755605021665493184937984
%N a(n) = n!/2-(-2)^(n-2)*(n-2).
%C "Number of positive terms in the ordinary development of a determinant having negative elements in the diagonal and positive elements elsewhere." [Muir]
%D T. Muir, A Treatise on the Theory of Determinants. Dover, NY, 1960, Sect. 132, p. 115.
%F E.g.f.: (1/(1 - x) + (1 + x)*exp(-2*x))/2. - _Ilya Gutkovskiy_, Aug 17 2016
%p f:=n->n!/2-(-2)^(n-2)*(n-2); [seq(f(n),n=0..40)];
%t Table[n!/2 - (-2)^(n - 2)*(n - 2), {n, 0, 25}] (* _Wesley Ivan Hurt_, Aug 17 2016 *)
%o (Magma) [Factorial(n)/2 - (-2)^(n - 2)*(n - 2) : n in [0..30]]; // _Wesley Ivan Hurt_, Aug 17 2016
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Feb 24 2011
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