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 A153731 Triangle read by rows: nonzero coefficients of Swinnerton-Dyer polynomials. 2

%I

%S -2,1,1,-10,1,576,-960,352,-40,1,46225,-5596840,13950764,-7453176,

%T 1513334,-141912,6476,-136,1,2000989041197056,-44660812492570624,

%U 183876928237731840,-255690851718529024,172580952324702208

%N Triangle read by rows: nonzero coefficients of Swinnerton-Dyer polynomials.

%D Roman E. Maeder. Programming in Mathematica, Addison-Wesley, 1990, page 105.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Swinnerton-DyerPolynomial.html">Swinnerton-Dyer Polynomial</a>

%e First few rows are:

%e -2, 1;

%e 1, -10, 1;

%e 576, -960, 352, -40, 1;

%e 46225, -5596840, 13950764, -7453176, 1513334, -141912, 6476, -136, 1;

%e ....

%e -2 + x^2, 1 - 10*x^2 + x^4, 576 - 960*x^2 + 352*x^4 - 40*x^6 + x^8, ...

%t SwinnertonDyerP[0, x_ ] := x; SwinnertonDyerP[n_, x_ ] := Module[{sd, srp = Sqrt[Prime[n]]}, sd[y_] = SwinnertonDyerP[n - 1, y]; Expand[ sd[x + srp] sd[x - srp] ] ]; row[n_] := CoefficientList[ SwinnertonDyerP[n, x], x^2]; Table[row[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Nov 09 2012 *)

%o (Julia)

%o using Nemo

%o function A153731Row(n)

%o R, x = PolynomialRing(ZZ, "x")

%o p = swinnerton_dyer(n, x)

%o [coeff(p, j) for j in 0:2:2^n] end

%o for n in 1:4 A153731Row(n) |> println end # _Peter Luschny_, Mar 13 2018

%K sign,tabf

%O 1,1

%A _Eric W. Weisstein_, Dec 31 2008

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Last modified August 17 03:29 EDT 2018. Contains 313810 sequences. (Running on oeis4.)