OFFSET
0,2
COMMENTS
Denominator of n-th derivative is (1+x^2)^(n+1), whose coefficients are the binomial coefficients, A007318.
FORMULA
For 0<=k<=n, let a(n, k) be the coefficient of x^k in the numerator of the n-th derivative of 1/(1+x^2). If n+k is even, a(n, k) = (-1)^((n+k)/2)*n!*binomial(n+1, k); if n+k is odd, a(n, k)=0.
EXAMPLE
The coefficients of the numerators starting with the coefficient of the highest power of x are 1; -2,0; 6,0,-2; -24,0,24,0; ...
MATHEMATICA
a[n_, k_] := Coefficient[Expand[Together[(1+x^2)^(n+1)*D[1/(1+x^2), {x, n}]]], x, k]; Flatten[Table[a[n, k], {n, 0, 10}, {k, n, 0, -1}]]
CROSSREFS
KEYWORD
AUTHOR
Mohammad K. Azarian, Nov 05 2002
EXTENSIONS
Edited by Dean Hickerson, Nov 28 2002
STATUS
approved