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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":"The row polynomials satisfy P(n,x) = (2+2*x)*P(n-2,x) - (1-2*x+x^2)*P(n-4,x) for n >= 4, with P(0,x) = 1, P(1,x) = 1, P(2,x) = 1 + x, P(3,x) = 3 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1;\nP[2, x_] := 1 + x;\nP[3, x_] := 3 + x;\nP[n_, x_] := P[n, x] = Expand[(2 + 2*x)*P[n - 2, x] - (1 - 2*x + x^2)*P[n - 4, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 1; v[3] = 1 + x; v[4] = 3 + x; for(n = 4, N, my(i = n + 1); v[i] = (2 + 2*x)*v[i - 2] - (1 - 2*x + x^2)*v[i - 4]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 1; v[3] = 1 + x; v[4] = 3 + x; for(n = 4, N, my(i = n + 1); v[i] = (2 + 2*x)*v[i - 2] - (1 - 2*x + x^2)*v[i - 4]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = Vecrev(c); 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":true,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A109446","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","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":"The row polynomials satisfy P(n,x) = (2+2*x)*P(n-2,x) - (1-2*x+x^2)*P(n-4,x) for n >= 4, with P(0,x) = 1, P(1,x) = 1, P(2,x) = 1 + x, P(3,x) = 3 + 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