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A156926
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Row sums of the FP2 polynomials of A156925.
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1
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1, 2, -8, -96, 4608, 1105920, -1592524800, -16052649984000, 1294485694709760000, 939485937792555417600000, -6818413142123250198773760000000, -544338467423010707068824846336000000000, 521477993674340011006196823029396275200000000000
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OFFSET
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0,2
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COMMENTS
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|a(n)| is the 2^n times the determinant of the n X n matrix whose element (i,j) equals i^j. - Michel Lagneau, Feb 08 2021
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LINKS
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FORMULA
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Row sum(n+1) = (-1)^(n)*2*(n+1)!*Row sum(n) with Row sum(n=0) = 1.
Let A(x)=sum(k>=0, |a(k)|*x^k ), then A(x)= G(0)/2, where G(k)= 1 + 1/(1 - 2*x*(k+1)!/(2*x*(k+1)! + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 10 2013
Let A(x)=sum(k>=0, |a(k)|*x^k ), then A(x)= G(0)/(4*x)- 1/(2*x), where G(k)= 1 + 1/(1 - 2*x*(2*k)!/(2*x*(2*k)! + 1/(1 + 1/(1 - 2*x*(2*k+1)!/(2*x*(2*k+1)! + 1/G(k+1) ))))); (continued fraction). - Sergei N. Gladkovskii, Jul 10 2013
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 1, -2*n!*a(n-1)*(-1)^n)
end:
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PROG
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(PARI) for(n=0, 12, print1((-1)^(n\2)*2^n*matdet(matrix(n, n, i, j, i^j)), ", ")) \\ Hugo Pfoertner, Feb 09 2021
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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