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 A076741 Nonzero coefficients of the polynomials in the numerator of 1/(1+x^2) and its successive derivatives, starting with the constant term. 3
 1, -2, -2, 6, 24, -24, 24, -240, 120, -720, 2400, -720, -720, 15120, -25200, 5040, 40320, -282240, 282240, -40320, 40320, -1451520, 5080320, -3386880, 362880, -3628800, 43545600, -91445760, 43545600, -3628800, -3628800, 199584000, -1197504000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Denominator of n-th derivative is (1+x^2)^(n+1), whose coefficients are the binomial coefficients, A007318. REFERENCES Roland Zumkeller, Formal global optimization with Taylor models, IJCAR (Ulrich Furbach and Natara jan Shankar, eds.), Lecture Notes in Computer Science, vol. 4130, Springer, 2006, pp. 408-422. LINKS Roland Zumkeller, Formal global optimization with Taylor models, Preprint, 2006. Roland Zumkeller, Formal global optimization with Taylor models, Thesis 2006. 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 nonzero coefficients of the numerators starting with the constant term are: 1; -2; -2,6; 24,-24; ... MATHEMATICA a[n_, k_] := Coefficient[Expand[Together[(1+x^2)^(n+1)*D[1/(1+x^2), {x, n}]]], x, k]; Select[Flatten[Table[a[n, k], {n, 0, 10}, {k, 0, n}]], #!=0&] CROSSREFS Cf. A076256, A076257, A076743. Sequence in context: A069466 A143084 A188962 * A320603 A276409 A093453 Adjacent sequences:  A076738 A076739 A076740 * A076742 A076743 A076744 KEYWORD sign,tabf,easy AUTHOR Mohammad K. Azarian, Nov 11 2002 EXTENSIONS Edited by Dean Hickerson, Nov 28 2002 STATUS approved

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Last modified October 3 14:34 EDT 2022. Contains 357237 sequences. (Running on oeis4.)