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Search: id:A162014
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| A162014 |
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Sequence related to the o.g.f.s. of the right hand columns of the EG1 triangle A162005. |
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+0
6
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| 1, 8, -1536, -14155776, 10436770529280, 923378661099307008000, -13724698564186788948502118400000, -45695540009113634492156662349750599680000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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a(n) = (-1)^( (n^2+n-2)/2)*4^((n-1)*n/2)*n!*product(k!, k=0..n-1)^2
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EXAMPLE
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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
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CROSSREFS
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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: A064073 A096970 A114617 this_sequence A160231 A163017 A017295
Adjacent sequences: A162011 A162012 A162013 this_sequence A162015 A162016 A162017
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KEYWORD
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easy,sign
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AUTHOR
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Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009
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