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v[1] = 1; for(n = 2, N, my(i = n); v[i] = -(n - 2 - x)*v[i - 1] - x*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":"A111596","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: 0,      1;\n  2: 0,     -2,        1;\n  3: 0,      6,       -6,       1;\n  4: 0,    -24,       36,     -12,       1;\n  5: 0,    120,     -240,     120,     -20,      1;\n  6: 0,   -720,     1800,   -1200,     300,    -30,      1;\n  7: 0,   5040,   -15120,   12600,   -4200,    630,    -42,    1;\n  8: 0, -40320,   141120, -141120,   58800, -11760,   1176,  -56,   1;\n  9: 0, 362880, -1451520, 1693440, -846720, 211680, -28224, 2016, -72, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(n-1-x)*P(n-1,x) - x*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[-(n - 1 - x)*P[n - 1, x] - x*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)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = -(n - 1 - x)*v[i - 1] - x*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":1,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-01897e65d9bb3867","steps":["x \u21a6 \u2212x\u22121"],"edges":["e-78ddaa76e5b8e8bc"],"text":"A059110 \u2192 x \u21a6 \u2212x\u22121"},"headline":"A111596: The matrix inverse of the unsigned Lah numbers A271703.","chain":"A059110 \u2192 x \u21a6 \u2212x\u22121"}