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