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A162014 Sequence related to the o.g.f.s. of the right hand columns of the EG1 triangle A162005.

%I A162014 #2 Mar 30 2012 18:59:45
%S A162014 1,8,-1536,-14155776,10436770529280,923378661099307008000,
%T A162014 -13724698564186788948502118400000,
%U A162014 -45695540009113634492156662349750599680000000
%N A162014 Sequence related to the o.g.f.s. of the right hand columns of the EG1 triangle A162005.
%C A162014 The a(n) are the sums of the coefficients of the polynomials that appear in the numerators of the o.g.f.s. of the right hand columns of the EG1 triangle A162005, see the examples.
%F A162014 a(n) = (-1)^( (n^2+n-2)/2)*4^((n-1)*n/2)*n!*product(k!, k=0..n-1)^2
%e A162014 The polynomials in the numerators of the first few o.g.f.s are:
%e A162014 numer(GF(1)) = 1
%e A162014 numer(GF(2)) = 2+6*z
%e A162014 numer(GF(3)) = 16+296*z-768*z^2-1080*z^3
%e A162014 numer(GF(4)) = 272+17376*z-321360*z^2-1298624*z^3+8914800*z^4-11262240*z^5-10206000*z^6
%e A162014 numer(GF(5)) = 7936 + 1305088*z - 79792256*z^2 - 109331968*z^3 + 41828672000*z^4-460917924352*z^5 + 238697445120*z^6 + 5066784271872*z^7 - 14723693948160*z^8+ 12172737024000*z^9 + 8101522800000*z^10
%Y A162014 A000012, A004004 (2x), A162008, A162009 and A162010 are the first five right hand columns of the EG1 triangle A162005.
%Y A162014 Cf. A055209 and A059332.
%K A162014 easy,sign
%O A162014 1,2
%A A162014 _Johannes W. Meijer_, Jun 27 2009