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v[1] = 1; for(n = 2, N, my(i = n); v[i] = (1 - x)*v[i - 1] + (x - x^2)*deriv(v[i - 1], x)); 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":"A163626","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,   -1;\n  2: 1,   -3,     2;\n  3: 1,   -7,    12,      -6;\n  4: 1,  -15,    50,     -60,      24;\n  5: 1,  -31,   180,    -390,     360,     -120;\n  6: 1,  -63,   602,   -2100,    3360,    -2520,     720;\n  7: 1, -127,  1932,  -10206,   25200,   -31920,   20160,    -5040;\n  8: 1, -255,  6050,  -46620,  166824,  -317520,  332640,  -181440,   40320;\n  9: 1, -511, 18660, -204630, 1020600, -2739240, 4233600, -3780000, 1814400, -362880;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1-x)*P(n-1,x) + (x-x^2)*d/dx P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(1 - x)*P[n - 1, x] + (x - x^2)*D[P[n - 1, x], 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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