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183720,   1713324,    9638320,    36419280,     97355520,    188743360,     267321600,     274444800,     199127040,       96897024,       28385280,        3784704;\n  7:   48639,  1160194,  12800060,   86561160,   400793008,   1343864480,   3364482240,    6388086400,    9241648640,   10135802880,     8294221824,     4909707264,     1986969600,     492011520,      56229888;\n  8:  265729,  7245856,  92309920,  729237376,  3997885696,  16126136320,  49501204480,  117939742720,  220391760640,  324045680640,   373583745024,   334109884416,   227205242880,  113556258816,   39332806656,    8434483200,    843448320;\n  9: 1462563, 44874954, 648295272, 5858890176, 37114530048, 174989283840, 636330240000, 1824612710400, 4181764942080, 7716832898560, 11491931547648, 13776668319744, 13195012841472, 9958952779776, 5792296992768, 2504760360960, 758260039680, 143386214400, 12745441280;\n","recurrence_sentence":"The row polynomials satisfy n*P(n,x) = -(n-1+(4*n-4)*x+(4*n-4)*x^2)*P(n-2,x) + (6*n-3+(20*n-10)*x+(16*n-8)*x^2)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 3 + 10*x + 8*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + 10*x + 8*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[(-(n - 1 + (4*n - 4)*x + (4*n - 4)*x^2)*P[n - 2, x] + (6*n - 3 + (20*n - 10)*x + (16*n - 8)*x^2)*P[n - 1, x])/(n)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3 + 10*x + 8*x^2; for(n = 2, N, my(i = n + 1); v[i] = (-(n - 1 + (4*n - 4)*x + (4*n - 4)*x^2)*v[i - 2] + (6*n - 3 + (20*n - 10)*x + (16*n - 8)*x^2)*v[i - 1])/(n)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-e4d248920a317259","steps":["basis A013609"],"edges":["e-94bde939ea1457ab"],"text":"A109983 \u2192 basis A013609"},"headline":"A109983 \u2192 basis 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