OFFSET
0,2
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
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
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
PROG
(PARI) for(n=0, 12, print1((-1)^(n\2)*2^n*matdet(matrix(n, n, i, j, i^j)), ", ")) \\ Hugo Pfoertner, Feb 09 2021
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Johannes W. Meijer, Feb 20 2009
STATUS
approved