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

0,2

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

Table of n, a(n) for n=0..18.

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.

Formula

G.f.: -(90194313216*t^11 -15300820992*t^10 -1979711488*t^9 -292552704*t^8 -22216704*t^7 +10649600*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).

Crossrefs

Cf. A246036, A271494, A271496.

Sequence in context: A169712 A235488 A199829 * A232587 A027804 A212236

Adjacent sequences: A271492 A271493 A271494 * A271496 A271497 A271498

Keyword

nonn

Author

N. J. A. Sloane, Apr 15 2016

Status

approved