Let's analyze the Noam Zeilberger sequences
where The i-th entry is the coefficient of z^(2*i-1) in L_ind(z,x) defined i\
n Eq. (6) of Noam Zeilberger's
article http://arxiv.org/abs/1512.06751
File http://www.math.rutgers.edu/~zeilberg/tokhniot/onoam2.txt
gives the first 301 terms of this sequence of polynomials
It seems to be asymptotically C*n!*6^n times constant
The last 10 terms (291 through 300) of Noam0(n)/n!/6^n are
[0.3503564894, 0.3503597295, 0.3503629473, 0.3503661432, 0.3503693173,
0.3503724699, 0.3503756012, 0.3503787114, 0.3503818007, 0.3503848693]
The sequence of averages seems to be linear, the last 10 terms of the averag\
e divided by n is
[.1419765076, .1417357928, .1414963030, .1412580279, .1410209571, .1407850806,
.1405503882, .1403168703, .1400845169, .1398533184]
The sequence of variances seems to also be linear , the last 10 terms of the\
average divided by n is
[.1401040189, .1398699986, .1396371560, .1394054814, .1391749648, .1389455969,
.1387173678, .1384902684, .1382642892, .1380394210]
Finally the random variable counted by the exponent of x seems to be asympt\
otically normal. Indeed
The sequence of skewness is:
[.1522660124, .1521407059, .1520159176, .1518916434, .1517678795, .1516446223,
.1515218682, .1513996132, .1512778536, .1511565862]
The sequence of kurtotis is:
[3.022409763, 3.022374652, 3.022339707, 3.022304927, 3.022270311, 3.022235856,
3.022201563, 3.022167430, 3.022133455, 3.022099637]
The sequence of standardized fifth moment is:
[1.525684296, 1.524424971, 1.523170857, 1.521921914, 1.520678103, 1.519439389,
1.518205733, 1.516977098, 1.515753445, 1.514534743]
The sequence of standardized sixth moment is:
[15.56830086, 15.56739233, 15.56648818, 15.56558838, 15.56469289, 15.56380167,
15.56291470, 15.56203193, 15.56115334, 15.56027889]