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%I #6 Oct 08 2013 02:41:20
%S 1,1,0,-1,-1,3,-2,25,-213,1547,-13276,129069,-1375775,16009741,
%T -202184274,2753591087,-40231298023,627731583225,-10418193719432,
%U 183264681827863,-3406106373633009,66695477905719251,-1372395141298236250,29607108539572186329
%N Difference between number of even equivalence classes and odd classes of terms in a symmetric determinant of order n.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #12, a'_n.
%F E.g.f.: exp(1/2*t-1/4*t^2)*(1+t)^(1/2)
%F a(n) ~ (-1)^(n+1) * n^(n-1) / (sqrt(2)*exp(n+3/4)). - _Vaclav Kotesovec_, Oct 07 2013
%t CoefficientList[Series[E^(1/2*x-1/4*x^2)*(1+x)^(1/2), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 07 2013 *)
%Y Cf. A002135.
%K sign
%O 0,6
%A _N. J. A. Sloane_, Jan 30 2001
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