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v[1] = 1; v[2] = 1 - 2*x; for(n = 3, N, my(i = n); v[i] = (2*n - 3 - (2*n - 2)*x)*v[i - 1] - (n^2 - 4*n + 4 - (2*n^2 - 8*n + 8)*x + (n^2 - 4*n + 4)*x^2)*v[i - 2]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A123202","target":"triangle","first_row":1,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:      1;\n  1:      1,       -2;\n  2:      2,       -8,        7;\n  3:      6,      -36,       63,        -34;\n  4:     24,     -192,      504,       -544,       209;\n  5:    120,    -1200,     4200,      -6800,      5225,      -1546;\n  6:    720,    -8640,    37800,     -81600,     94050,     -55656,     13327;\n  7:   5040,   -70560,   370440,    -999600,   1536150,   -1363572,    653023,    -130922;\n  8:  40320,  -645120,  3951360,  -12794880,  24578400,  -29089536,  20896736,   -8379008,   1441729;\n  9: 362880, -6531840, 45722880, -172730880, 398170080, -589063104, 564211872, -339349824, 116780049, -17572114;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2*n-1-2*n*x)*P(n-1,x) - (n^2-2*n+1-(2*n^2-4*n+2)*x+(n^2-2*n+1)*x^2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1 - 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 - 2*x;\nP[n_, x_] := P[n, x] = Expand[(2*n - 1 - 2*n*x)*P[n - 1, x] - (n^2 - 2*n + 1 - (2*n^2 - 4*n + 2)*x + (n^2 - 2*n + 1)*x^2)*P[n - 2, x]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); 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