A156926 Row sums of the FP2 polynomials of A156925.

1, 2, -8, -96, 4608, 1105920, -1592524800, -16052649984000, 1294485694709760000, 939485937792555417600000, -6818413142123250198773760000000, -544338467423010707068824846336000000000, 521477993674340011006196823029396275200000000000

Offset: 0

Author

Johannes W. Meijer, Feb 20 2009

Keywords

• easy
• sign

Comments

|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

Crossrefs

Row sums of A156925.

Cf. A000079, A000178, A057077.

Programs

Maple

a:= proc(n) option remember;
      `if`(n=0, 1, -2*n!*a(n-1)*(-1)^n)
    end:
seq(a(n), n=0..14);  # Alois P. Heinz, Feb 09 2021

PARI

for(n=0,12,print1((-1)^(n\2)*2^n*matdet(matrix(n,n,i,j,i^j)),", ")) \\ Hugo Pfoertner, Feb 09 2021

Formula

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

a(n) = A000079(n) * A000178(n) * A057077(n). - Alois P. Heinz, Feb 09 2021