Numerics for the combinatorial Random variable, "Number of occurrences of the pattern 321", defined in the samle space of, "123-avoiding n-permutations" By Shalosh B. Ekhad The input is the sequence of generating functions for the random variable, "Number of occurrences of the pattern 321", defined over the sample space, "123-avoiding n-permutations" for n from 1 to , 20 The sequence of averages is [0, 0, 1/5, 8/7, 24/7, 254/33, 6271/429, 17792/715, 95314/2431, 244874/4199, 2438265/29393, 5921640/52003, 28199044/185725, 4404130/22287, 2442949979/ 9694845, 5581985216/17678835, 8420058602/21607465, 56672025026/119409675, 100964850859/176726319, 372299317448/547010035] and in floating-point [0., 0., .2000000000, 1.142857143, 3.428571429, 7.696969697, 14.61771562, 24.88\ 391608, 39.20773344, 58.31721839, 82.95393461, 113.8711228, 151.8322466, 197.60\ 98174, 251.9844287, 315.7439512, 389.6828528, 474.6016186, 571.3062516, 680.607\ 8383] The sequence of variances is [0, 0, 4/25, 55/49, 631/147, 13529/1089, 5574128/184041, 33443671/511225, 761819717/5909761, 4165409953/17631601, 352660318708/863948449, 1816483576871/ 2704312009, 36591341605389/34493775625, 4017516024989/2483551845, 224953580596703744/93990019574025, 1078012650112678199/312541206957225, 6803372607484619383/1400647631178675, 95561974708205671049/14258670483605625, 1418055909128480919844/156160959136448805, 10866129308335967726693/ 897659935172103675] and in floating-point [0., 0., .1600000000, 1.122448980, 4.292517007, 12.42332415, 30.28742508, 65.41\ 869236, 128.9087185, 236.2468362, 408.1960204, 671.6989648, 1060.809985, 1617.6\ 49349, 2393.377314, 3449.185663, 4857.304904, 6702.025607, 9080.732579, 12104.9\ 5075] The , 3, -th alpha coefficients for n from, 15, to , 20, are : [-0.05184426721, -0.08185239491, -0.1081833461, -0.1315184395, -0.1523798024, -0.1711734346] The , 4, -th alpha coefficients for n from, 15, to , 20, are : [2.617942805, 2.623434620, 2.631212900, 2.640479288, 2.650688525, 2.661464621] The , 5, -th alpha coefficients for n from, 15, to , 20, are : [-0.2727809478, -0.5199966757, -0.7379943835, -0.9324484755, -1.107614843, -1.266742827] The , 6, -th alpha coefficients for n from, 15, to , 20, are : [10.22453481, 10.28565675, 10.38390097, 10.50695132, 10.64640529, 10.79645208] This ends this numerical short article.