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A156926 Row sums of the FP2 polynomials of A156925. 1

%I

%S 1,2,-8,-96,4608,1105920,-1592524800,-16052649984000,

%T 1294485694709760000,939485937792555417600000,

%U -6818413142123250198773760000000,-544338467423010707068824846336000000000,521477993674340011006196823029396275200000000000

%N Row sums of the FP2 polynomials of A156925.

%C |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

%F Row sum(n+1) = (-1)^(n)*2*(n+1)!*Row sum(n) with Row sum(n=0) = 1.

%F 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

%F 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

%F a(n) = A000079(n) * A000178(n) * A057077(n). - _Alois P. Heinz_, Feb 09 2021

%p a:= proc(n) option remember;

%p `if`(n=0, 1, -2*n!*a(n-1)*(-1)^n)

%p end:

%p seq(a(n), n=0..14); # _Alois P. Heinz_, Feb 09 2021

%o (PARI) for(n=0,12,print1((-1)^(n\2)*2^n*matdet(matrix(n,n,i,j,i^j)),", ")) \\ _Hugo Pfoertner_, Feb 09 2021

%Y Row sums of A156925.

%Y Cf. A000079, A000178, A057077.

%K easy,sign

%O 0,2

%A _Johannes W. Meijer_, Feb 20 2009

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Last modified June 17 15:34 EDT 2021. Contains 345084 sequences. (Running on oeis4.)