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

1,2

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.

Links

Table of n, a(n) for n=1..8.

Formula

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

Example

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.

Sequence in context: A096970 A248386 A114617 * A300545 A300972 A300929

Adjacent sequences: A162011 A162012 A162013 * A162015 A162016 A162017

Keyword

easy,sign

Author

Johannes W. Meijer, Jun 27 2009

Status

approved