read `onoam2.txt`: read `HISTABRUT.txt`: print(`The Noam Zeilberger sequence `): print(): print(`--------------------------`): print(): print(time()): print(`Let's analyze the Noam Zeilberger sequences `): print(`where The i-th entry is the coefficient of z^(2*i-1) in L_ind(z,x) defined in Eq. (6) of Noam Zeilberger's `): print(` article http://arxiv.org/abs/1512.06751 `): print(`File http://www.math.rutgers.edu/~zeilberg/tokhniot/onoam2.txt `): print(`gives the first 301 terms of this sequence of polynomials`): print(`It seems to be asymptotically C*n!*6^n times constant`): print(`The last 10 terms (291 through 300) of Noam0(n)/n!/6^n are `): print(): print(evalf([seq(Noam0[i+1]/i!/6^i,i=291..300)],10)): print(``): lu:=[seq(evalf(Alpha(NoamX[i+1],x,6)),i=291..300)]: print(`The sequence of averages seems to be linear, the last 10 terms of the average divided by n is`): lprint([seq(lu[i][1]/(i+290),i=1..nops(lu))]): print(`The sequence of variances seems to also be linear , the last 10 terms of the average divided by n is`): print(``): lprint([seq(lu[i][2]/(i+290),i=1..nops(lu))]): print(``): print(`Finally the random variable counted by the exponent of x seems to be asymptotically normal. Indeed `): print(`The sequence of skewness is:`): print(``): lprint([seq(lu[i][3],i=1..nops(lu))]): print(``): print(`The sequence of kurtotis is:`): print(``): lprint([seq(lu[i][4],i=1..nops(lu))]): print(``): print(`The sequence of standardized fifth moment is:`): print(``): lprint([seq(lu[i][5],i=1..nops(lu))]): print(``): print(``): print(`The sequence of standardized sixth moment is:`): print(``): lprint([seq(lu[i][6],i=1..nops(lu))]): quit: