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begins:\n  0: 1;\n  1: 1,        1;\n  2: 1,       14,          1;\n  3: 1,      111,        111,           1;\n  4: 1,      796,       2886,         796,            1;\n  5: 1,     5597,      52642,       52642,         5597,            1;\n  6: 1,    39210,     824271,     2000396,       824271,        39210,           1;\n  7: 1,   274507,   11931033,    58614299,     58614299,     11931033,      274507,          1;\n  8: 1,  1921592,  165260188,  1483533704,   2930714950,   1483533704,   165260188,    1921592,        1;\n  9: 1, 13451193, 2231010900, 34301767332, 119257418574, 119257418574, 34301767332, 2231010900, 13451193, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+(6*n-5)*x)*P(n-1,x) + (6*x-6*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 + (6*n - 5)*x)*P[n - 1, x] + (6*x - 6*x^2)*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = 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    1;\n   9: 1,  1921592,  165260188,  1483533704,   2930714950,   1483533704,   165260188,    1921592,        1;\n  10: 1, 13451193, 2231010900, 34301767332, 119257418574, 119257418574, 34301767332, 2231010900, 13451193, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+(6*n-11)*x)*P(n-1,x) + (6*x-6*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 + (6*n - 11)*x)*P[n - 1, x] + (6*x - 6*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 + (6*n - 11)*x)*v[i - 1] + (6*x - 6*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":"A142461","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,       14,          1;\n   4: 1,      111,        111,           1;\n   5: 1,      796,       2886,         796,            1;\n   6: 1,     5597,      52642,       52642,         5597,            1;\n   7: 1,    39210,     824271,     2000396,       824271,        39210,           1;\n   8: 1,   274507,   11931033,    58614299,     58614299,     11931033,      274507,          1;\n   9: 1,  1921592,  165260188,  1483533704,   2930714950,   1483533704,   165260188,    1921592,        1;\n  10: 1, 13451193, 2231010900, 34301767332, 119257418574, 119257418574, 34301767332, 2231010900, 13451193, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (1+(6*n-11)*x)*P(n-1,x) + (6*x-6*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 + (6*n - 11)*x)*P[n - 1, x] + (6*x - 6*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 + (6*n - 11)*x)*v[i - 1] + (6*x - 6*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-3bc26d3108ee6bfd","steps":[],"edges":[],"text":"A142461"},"headline":"A142461: Triangle read by rows: T(n,k) (1 <= k <= n) given by T(n, 1) = T(n,n) = 1, otherwise 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