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54377008,    671838,       1;\n  10: 1, 4031069, 622333256, 9346191344, 32208325226, 32208325226, 9346191344, 622333256, 4031069, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+(5*n-9)*x)*P(n-1,x) + (5*x-5*x^2)*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(1 + (5*n - 9)*x)*P[n - 1, x] + (5*x - 5*x^2)*D[P[n - 1, x], x]];\nTable[PadRight[CoefficientList[P[n, x], x], n], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = (1 + (5*n - 9)*x)*v[i - 1] + (5*x - 5*x^2)*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":0,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A142460","target":"reversed_triangle","first_row":0,"oeis_offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   1: 1;\n   2: 1,       1;\n   3: 1,      12,         1;\n   4: 1,      83,        83,          1;\n   5: 1,     514,      1826,        514,           1;\n   6: 1,    3105,     28310,      28310,        3105,           1;\n   7: 1,   18656,    376615,     905920,      376615,       18656,          1;\n   8: 1,  111967,   4627821,   22403635,    22403635,     4627821,     111967,         1;\n   9: 1,  671838,  54377008,  478781506,   940952670,   478781506,   54377008,    671838,       1;\n  10: 1, 4031069, 622333256, 9346191344, 32208325226, 32208325226, 9346191344, 622333256, 4031069, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (1+(5*n-9)*x)*P(n-1,x) + (5*x-5*x^2)*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(1 + (5*n - 9)*x)*P[n - 1, x] + (5*x - 5*x^2)*D[P[n - 1, x], x]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n]], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = (1 + (5*n - 9)*x)*v[i - 1] + (5*x - 5*x^2)*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":0,"offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-05516f61aeaea779","steps":[],"edges":[],"text":"A142460"},"headline":"A142460: Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), 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