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

1, 8, -1536, -14155776, 10436770529280, 923378661099307008000, -13724698564186788948502118400000, -45695540009113634492156662349750599680000000

Offset: 1

Author

Johannes W. Meijer, Jun 27 2009

Keywords

• easy
• sign

Comments

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.

Examples

			The polynomials in the numerators of the first few o.g.f.s are:
numer(GF(1)) = 1
numer(GF(2)) = 2+6*z
numer(GF(3)) = 16+296*z-768*z^2-1080*z^3
numer(GF(4)) = 272+17376*z-321360*z^2-1298624*z^3+8914800*z^4-11262240*z^5-10206000*z^6
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
		

Crossrefs

A000012, A004004 (2x), A162008, A162009 and A162010 are the first five right hand columns of the EG1 triangle A162005.

Cf. A055209 and A059332.

Formula

a(n) = (-1)^( (n^2+n-2)/2)*4^((n-1)*n/2)*n!*product(k!, k=0..n-1)^2