The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001782 Discriminants of Shapiro polynomials. (Formerly M5286 N2301) 5
 1, -44, -4940800, -564083990621761115783168, -265595429519150677725101890892978815884074732203939261150723571712 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Sean A. Irvine, Table of n, a(n) for n = 1..8 Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics 36(2), 2007, pp. 251-257. MR2312537.  Zbl 1133.11012. John Brillhart and L. Carlitz, Note on the Shapiro polynomials, Proceedings of the American Mathematical Society, volume 25, number 1, May 1970, pages 114-118.  Also at JSTOR, or annotated scanned copy. Robert Davis, Greg Simay, Further Combinatorics and Applications of Two-Toned Tilings, arXiv:2001.11089 [math.CO], 2020. FORMULA Let P_0(x) = Q_0(x) = 1. For n > 0, P_{n + 1}(x) = P_n(x) + x^(2^n)*Q_n(x) and Q_{n + 1}(x) = P_n(x) - x^(2^n)*Q_n(x). Then, a(n) = discrim(P_n(x)). Note also that discrim(P_n(x)) = discrim(Q_n(x)). - Sean A. Irvine, Nov 25 2012 PROG (PARI) a(n) = my(P=Pol(1), Q=1); for(i=0, n-1, [P, Q]=[P+'x^(2^i)*Q, P-'x^(2^i)*Q]); poldisc(P); \\ Kevin Ryde, Feb 23 2020 CROSSREFS See A020985 for the Shapiro polynomials.  Cf. A331691 (P,Q resultant). Sequence in context: A115734 A119078 A172878 * A172910 A119058 A218402 Adjacent sequences:  A001779 A001780 A001781 * A001783 A001784 A001785 KEYWORD sign,nice AUTHOR EXTENSIONS Extended by Sean A. Irvine, Nov 25 2012 STATUS approved

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

Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)