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A166243 Villegas-Zagier polynomials (listing coefficients from lowest to highest degree). 4
0, 1, 0, 0, -3, 0, 2, 0, 0, 9, -2, 0, 0, -18, 0, 0, -27, 0, 0, 36, 0, 0, 108, 0, 0, 81, 0, 152, 0, 0, -360, 0, 0, -540, 0, 0, -243, -152, 0, 0, -16440, 0, 0, 2700, 0, 0, 2430, 0, 0, 729, 0, 0, 24240, 0, 0, 1311840, 0, 0, -17010, 0, 0, -10206, 0, 0, -2187, 0, 6848, 0, 0, -2974800 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

REFERENCES

H. Cohen, Number Theory. Volume I: Tools and Diophantine Equations, Springer-Verlag, 2007, p. 378.

LINKS

Seiichi Manyama, Rows n = -1..99, flattened

FORMULA

V(-1) = 0, V(0) = 1, and for n >= 0, V(n+1) = (8*x^3-1)*V'(n) - (16*n+3)*x^2*V(n) - 4*n*(2*n-1)*x*V(n-1).

EXAMPLE

V(-1) = 0;

V(0) = 1;

V(1) = 0 + 0*x - 3*x^2;

V(2) = 0 + 2*x + 0*x^2 + 0*x^3 + 9*x^4.

PROG

(PARI) { V(n) = my(p0, p1, q); if(n==-1, return(0)); p0 = 0; p1 = 1; for(m=1, n, q = (8*x^3-1)*deriv(p1) - (16*(m-1)+3)*x^2*p1 - 4*(m-1)*(2*(m-1)-1)*x*p0; p0 = p1; p1 = q; ); p1; }

CROSSREFS

Cf. A166244, A159843, A166246, A206309.

Sequence in context: A067169 A257927 A011339 * A118514 A190544 A172293

Adjacent sequences:  A166240 A166241 A166242 * A166244 A166245 A166246

KEYWORD

sign,tabf

AUTHOR

Max Alekseyev, Oct 10 2009

STATUS

approved

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Last modified April 16 11:58 EDT 2021. Contains 343037 sequences. (Running on oeis4.)