A006309 Coefficients of period polynomials.

1, 5, -21, 33, -65, 85, -133, 161, 261, -341, -481, 533, -645, 705, 901, -12803, -1281, -1541, 1633, -1825, -14615, -11537, 2581, -3201, 3333

Offset: 2

Author

N. J. A. Sloane

Keywords

• sign
• more

References

• D. H. and Emma Lehmer, Cyclotomy for nonsquarefree moduli, pp. 276-300 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• David Naccache and Ofer Yifrach-Stav, Pattern Recognition Experiments on Mathematical Expressions, arXiv:2301.01624 [math.NT], 2022.
• Ofer Yifrach-Stav, Fast and Private Pool Testing and Contributions to Experimental Mathematics, Doctoral thesis, École normale supérieure (Paris, France), HAL Science [math.cs] 2024, Art. No. tel-04513104. See pp. 108, 109, 212.

Formula

a(n) = [x^(p-3)] f(p,x) where p = A000040(n) and f(p,x) is defined in A006308. - Sean A. Irvine, Mar 07 2017

Extensions

More terms, signs added, and offset corrected by Sean A. Irvine, Mar 07 2017