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begins:\n  0: 0, 1;\n  1: 0, 1;\n  2: 0, 1,  1;\n  3: 0, 1,  3;\n  4: 0, 1,  6,   1;\n  5: 0, 1, 10,   5;\n  6: 0, 1, 15,  15,  1;\n  7: 0, 1, 21,  35,  7;\n  8: 0, 1, 28,  70, 28, 1;\n  9: 0, 1, 36, 126, 84, 9;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = 2*P(n-1,x) - (1-x)*P(n-2,x) for n >= 2, with P(0,x) = x, P(1,x) = x.","mathematica":"P[0, x_] := x;\nP[1, x_] := x;\nP[n_, x_] := P[n, x] = Expand[2*P[n - 1, x] - (1 - x)*P[n - 2, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = x; v[2] = x; for(n = 2, N, my(i = n + 1); v[i] = 2*v[i - 1] - (1 - x)*v[i - 2]); 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}},{"oeis_id":"A034839","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"low","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0: 1;\n  1: 1;\n  2: 1,  1;\n  3: 1,  3;\n  4: 1,  6,   1;\n  5: 1, 10,   5;\n  6: 1, 15,  15,  1;\n  7: 1, 21,  35,  7;\n  8: 1, 28,  70, 28, 1;\n  9: 1, 36, 126, 84, 9;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in ascending powers of x, starting at the lowest nonzero coefficient, where P(n,x) = 2*P(n-1,x) - (1-x)*P(n-2,x) for n >= 2, with P(0,x) = x, P(1,x) = x.","mathematica":"P[0, x_] := x;\nP[1, x_] := x;\nP[n_, x_] := P[n, x] = Expand[2*P[n - 1, x] - (1 - x)*P[n - 2, x]];\nTable[CoefficientList[Expand[P[n, x]/x^Exponent[P[n, x], x, Min]], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = x; v[2] = x; for(n = 2, N, my(i = n + 1); v[i] = 2*v[i - 1] - (1 - x)*v[i - 2]); v};\nrow(n, p) = {my(c = Vecrev(p/x^valuation(p, x))); 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":"low","regular_triangle":false}},{"oeis_id":"A109446","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"low","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0: 1;\n  1: 1;\n  2: 1,  1;\n  3: 3,  1;\n  4: 1,  6,   1;\n  5: 5, 10,   1;\n  6: 1, 15,  15,  1;\n  7: 7, 35,  21,  1;\n  8: 1, 28,  70, 28, 1;\n  9: 9, 84, 126, 36, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, down to the lowest nonzero coefficient, where P(n,x) = 2*P(n-1,x) - (1-x)*P(n-2,x) for n >= 2, with P(0,x) = x, P(1,x) = x.","mathematica":"P[0, x_] := 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