The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A343445 Coefficients of the series S(p, q) for which (-sqrt(p))*S converges to the largest real root of x^3 - p*x + q for 0 < p and 0 < q < 2*(p/3)^(3/2). 1
 -1, 1, 3, 24, 315, 5760, 135135, 3870720, 130945815, 5109350400, 225881530875, 11158821273600, 609202488769875, 36422392637030400, 2366751668870964375, 166086110424858624000, 12517749576658530579375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Based on formulas for series solutions of trinomials given in Eagle article. LINKS Albert Eagle, Series for all the roots of a trinomial equation, Am. Math. Monthly, 46, no. 7 (Aug. - Sep., 1939), pp. 422-425. FORMULA a(n) = 2^(n - 1) * Gamma((3*n - 1)/2) / Gamma((n + 1)/2). a(n) = 2^(n - 1) * ((n + 1)/2)_(n - 1), where (x)_k is the Pochhammer symbol for Gamma(x + k) / Gamma(k). a(n) = 3*A113551(n-1) for n>=2. - Hugo Pfoertner, Apr 16 2021 E.g.f.: (sqrt(3)*sin(arcsin(3*sqrt(3)*x)/3) - 3*cos(arcsin(3*sqrt(3)*x)/3))/3. - Stefano Spezia, May 23 2021 MATHEMATICA Clear[a]; a = Table[2^(n - 1)Gamma[(3*n - 1)/2]/Gamma[(n + 1)/2], {n, 0, 20}] (* or equivalently *) Clear[a]; a = Table[2^(n - 1)Pochhammer[(n + 1)/2, n - 1], {n, 0, 20}] CROSSREFS Cf. A343446. Sequence in context: A075142 A138428 A047056 * A264561 A003236 A232693 Adjacent sequences:  A343442 A343443 A343444 * A343446 A343447 A343448 KEYWORD sign AUTHOR Dixon J. Jones, Apr 15 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)