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96, 72, 16, 1;\n 3: 125, 1206, 2161, 1280, 305, 30, 1;\n 4: 625, 14016, 50832, 59936, 30026, 7200, 856, 48, 1;\n 5: 3125, 157926, 1078561, 2260480, 2001130, 876300, 206002, 26880, 1925, 70, 1;\n 6: 15625, 1755936, 21759192, 76497456, 110250651, 78472800, 30648072, 6976656, 953427, 78400, 3760, 96, 1;\n 7: 78125, 19409046, 427487761, 2437774080, 5460005355, 5936010570, 3541828563, 1251060480, 274104735, 38222450, 3417827, 193536, 6657, 126, 1;\n 8: 390625, 213968256, 8277617952, 74989734976, 253540996276, 405358430400, 351906002448, 181033307424, 58440454278, 12288505600, 1721206720, 162115968, 10228148, 423360, 10960, 160, 1;\n 9: 1953125, 2355994566, 158986877761, 2257692462080, 11303335284980, 25919277354840, 31724602056484, 22851630835200, 10342581667230, 3076517535140, 620151630278, 86382870528, 8398136756, 570143448, 26745828, 844800, 17061, 198, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (5+6*x+x^2)*P(n-1,x) + (6*x+2*x^2)*d/dx P(n-1,x) + x^2*d^2/dx^2 P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(5 + 6*x + x^2)*P[n - 1, x] + (6*x + 2*x^2)*D[P[n - 1, x], x] + x^2*D[P[n - 1, x], {x, 2}]];\nTable[CoefficientList[P[n, x], x], {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] = (5 + 6*x + x^2)*v[i - 1] + (6*x + 2*x^2)*deriv(v[i - 1], x) + x^2*deriv(deriv(v[i - 1], x), x)); 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}}],"derivation":{"root":"n-b30e7a5b4198051a","steps":["basis A008277"],"edges":["e-8606f224a066b2e0"],"text":"A272866 \u2192 basis A008277"},"headline":"A272866 \u2192 basis A008277","chain":null}