|
Search: id:A076256
|
|
|
| A076256 |
|
Coefficients of the polynomials in the numerator of 1/(1+x^2) and its successive derivatives, starting with the constant term. |
|
+0
4
|
|
| 1, 0, -2, -2, 0, 6, 0, 24, 0, -24, 24, 0, -240, 0, 120, 0, -720, 0, 2400, 0, -720, -720, 0, 15120, 0, -25200, 0, 5040, 0, 40320, 0, -282240, 0, 282240, 0, -40320, 40320, 0, -1451520, 0, 5080320, 0, -3386880, 0, 362880, 0, -3628800, 0, 43545600, 0, -91445760, 0, 43545600
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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 constant term are 1; 0,-2; -2,0,6; 0,24,0,-24; ...
|
|
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, 0, n}]]
|
|
CROSSREFS
|
Cf. A076257, A076741, A076743.
Sequence in context: A088972 A100334 A129936 this_sequence A127467 A140333 A135006
Adjacent sequences: A076253 A076254 A076255 this_sequence A076257 A076258 A076259
|
|
KEYWORD
|
sign,tabl,easy
|
|
AUTHOR
|
Mohammad K. Azarian (azarian(AT)evansville.edu), Nov 05 2002
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Nov 28 2002
|
|
|
Search completed in 0.002 seconds
|
