A206309 Villegas-Zagier polynomial V(3*n) evaluated at x=0.

1, -2, -152, -6848, -8103296, 22483912960, -8062284861440, 196434444070666240, 532650564250569441280, 2039228675045199496806400, -5209573728611533514689740800, 1172773847164346785332278906060800, -14811687653648930753369603156895334400, -612441229040578815278149020969838051328000

Offset: 0

Author

Joerg Arndt, Feb 06 2012

Keywords

• sign

Comments

Numbers B_k in Villegas/Zagier "Which primes are sums of two cubes?"

References

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..156 (terms 0..66 from Vincenzo Librandi)
• Fernando Rodriguez Villegas, Don Zagier, Which primes are sums of two cubes?, CMS Conference Proceedings 15 (1995), pp. 295-306.

Crossrefs

The first column of A166243.

Cf. A166244, A159843, A166246

Programs

PARI

{ A206309(n) = my(p0, p1, q); p0 = 0; p1 = 1; for(m=1, 3*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; ); subst(p1,x,0); } \\ Max Alekseyev, Dec 05 2017

Extensions

Edited by Max Alekseyev, Dec 05 2017