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5685472296,        3211180848,          377913600;\n  7:     1567290800,     24486210960,     158929027632,      549405579276,     1071717884433,     1135047259368,       546492563856,       55553299200;\n  8:   117573742000,   2177743539600,   17239805555760,    75661171641612,   199160142593553,   315899350655400,    283714028584848,   119203770154752,    10666233446400;\n  9: 10932603994000, 234424251709200, 2193812144678520, 11706260938350624, 38985019550388801, 83125199704261707, 111351093204715848, 86948576426610864, 32433042017684736, 2591894727475200;\n","recurrence_sentence":"The row polynomials satisfy (n^2-2*n+1)*P(n,x) = -(n^6-4*n^5+8*n^4-8*n^3+4*n^2+(6*n^6-24*n^5+42*n^4-36*n^3+12*n^2)*x+(9*n^6-36*n^5+54*n^4-36*n^3+9*n^2)*x^2)*P(n-2,x) + (2*n^4-4*n^3+4*n^2-2*n+1+(6*n^4-12*n^3+6*n^2)*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 5 + 3*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 5 + 3*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(n^6 - 4*n^5 + 8*n^4 - 8*n^3 + 4*n^2 + (6*n^6 - 24*n^5 + 42*n^4 - 36*n^3 + 12*n^2)*x + (9*n^6 - 36*n^5 + 54*n^4 - 36*n^3 + 9*n^2)*x^2)*P[n - 2, x] + (2*n^4 - 4*n^3 + 4*n^2 - 2*n + 1 + (6*n^4 - 12*n^3 + 6*n^2)*x)*P[n - 1, x])/(n^2 - 2*n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 5 + 3*x; for(n = 2, N, my(i = n + 1); v[i] = (-(n^6 - 4*n^5 + 8*n^4 - 8*n^3 + 4*n^2 + (6*n^6 - 24*n^5 + 42*n^4 - 36*n^3 + 12*n^2)*x + (9*n^6 - 36*n^5 + 54*n^4 - 36*n^3 + 9*n^2)*x^2)*v[i - 2] + (2*n^4 - 4*n^3 + 4*n^2 - 2*n + 1 + (6*n^4 - 12*n^3 + 6*n^2)*x)*v[i - 1])/(n^2 - 2*n + 1)); 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-e734a631f8279507","steps":["basis A013610","D+1"],"edges":["e-5cbcb537f7289c2f","e-4babcb308764301b"],"text":"A008955 \u2192 basis A013610 \u2192 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