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A001782 Discriminants of Shapiro polynomials.
(Formerly M5286 N2301)
4
1, -44, -4940800, -564083990621761115783168, -265595429519150677725101890892978815884074732203939261150723571712 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257.  Mathematical Reviews, MR2312537.  Zentralblatt MATH, Zbl 1133.11012.

J. Brillhart and L. Carlitz, Note on the Shapiro polynomials, Pacific J. Math., 25 (1970), 114-118.

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

J. Brillhart and L. Carlitz, Note on the Shapiro polynomials [Annotated scanned copy]

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

CROSSREFS

See A020985 for the Shapiro polynomials.

Sequence in context: A115734 A119078 A172878 * A172910 A119058 A218402

Adjacent sequences:  A001779 A001780 A001781 * A001783 A001784 A001785

KEYWORD

sign,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended by Sean A. Irvine, Nov 25 2012

STATUS

approved

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Last modified November 21 15:00 EST 2019. Contains 329371 sequences. (Running on oeis4.)