A271495 Eighth moments of the Rudin-Shapiro polynomials.

1, 70, 668, 14104, 198640, 3420256, 53143488, 864838016, 13714054912, 220102985216, 3513567575040, 56284226394112, 900460612808704, 14414430456537088, 230619566685274112, 3689872453256970240, 59031392914560188416, 944463240632040030208, 15111217402853747064832

Offset: 0

Author

N. J. A. Sloane, Apr 15 2016

Keywords

• nonn

References

• Shalosh B. Ekhad, Explicit Generating Functions, Asymptotics, and More for the First 10 Even Moments of the Rudin-Shapiro Polynomials, Preprint, 2016.
• Doron Zeilberger, Personal Communication to N. J. A. Sloane, Apr 15 2016.

Links

• Christophe Doche, Even moments of generalized Rudin-Shapiro polynomials, Mathematics of computation 74.252 (2005): 1923-1935.
• Christophe Doche and Laurent Habsieger, Moments of the Rudin-Shapiro polynomials, Journal of Fourier Analysis and Applications 10.5 (2004): 497-505.

Crossrefs

Cf. A246036, A271494, A271496.

Formula

G.f.: -(90194313216*t^11 -15300820992*t^10 -1979711488*t^9 -292552704*t^8 -22216704*t^7 [phone]*t^6 -1024*t^5 -144384*t^4 +7008*t^3 +664*t^2 -54*t -1) / (8*t+1) / (16*t-1) / (1409286144*t^10 -264241152*t^9 -25690112*t^8 -4128768*t^7 -311296*t^6 +170496*t^5 -2624*t^4 -2208*t^3 +148*t^2 +8*t -1).