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3:  35,   210,   315,    140;\n  4:  70,   560,  1260,   1120,    350;\n  5: 126,  1260,  3780,   5040,   3150,    756;\n  6: 210,  2520,  9450,  16800,  15750,   7560,   1470;\n  7: 330,  4620, 20790,  46200,  57750,  41580,  16170,   2640;\n  8: 495,  7920, 41580, 110880, 173250, 166320,  97020,  31680,  4455;\n  9: 715, 12870, 77220, 240240, 450450, 540540, 420420, 205920, 57915, 7150;\n","recurrence_sentence":"The row polynomials satisfy (n+n^2*x)*P(n,x) = (n+4+(n^2+6*n+8)*x+(n^2+5*n+4)*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((n + 4 + (n^2 + 6*n + 8)*x + (n^2 + 5*n + 4)*x^2)*P[n - 1, x])/(n + n^2*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((n + 4 + (n^2 + 6*n + 8)*x + (n^2 + 5*n + 4)*x^2)*v[i - 1])/(n + n^2*x)); 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-79986ab5023c2764","steps":["\u03b8+1"],"edges":["e-597039afcb309e3c"],"text":"A178821 \u2192 \u03b8+1"},"headline":"A178821 \u2192 \u03b8+1","chain":null}