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row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A013622","target":"triangle","first_row":0,"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:     3,      5;\n  2:     9,     30,      25;\n  3:    27,    135,     225,     125;\n  4:    81,    540,    1350,    1500,      625;\n  5:   243,   2025,    6750,   11250,     9375,     3125;\n  6:   729,   7290,   30375,   67500,    84375,    56250,    15625;\n  7:  2187,  25515,  127575,  354375,   590625,   590625,   328125,    78125;\n  8:  6561,  87480,  510300, 1701000,  3543750,  4725000,  3937500,  1875000,   390625;\n  9: 19683, 295245, 1968300, 7654500, 19136250, 31893750, 35437500, 25312500, 10546875, 1953125;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3+5*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(3 + 5*x)*P[n - 1, 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] = (3 + 5*x)*v[i - 1]); 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":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A038245","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:       1;\n  1:       5,        3;\n  2:      25,       30,        9;\n  3:     125,      225,      135,       27;\n  4:     625,     1500,     1350,      540,       81;\n  5:    3125,     9375,    11250,     6750,     2025,      243;\n  6:   15625,    56250,    84375,    67500,    30375,     7290,     729;\n  7:   78125,   328125,   590625,   590625,   354375,   127575,   25515,    2187;\n  8:  390625,  1875000,  3937500,  4725000,  3543750,  1701000,  510300,   87480,   6561;\n  9: 1953125, 10546875, 25312500, 35437500, 31893750, 19136250, 7654500, 1968300, 295245, 19683;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (3+5*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(3 + 5*x)*P[n - 1, x]];\nTable[Reverse[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] = (3 + 5*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = Vecrev(c); 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":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-c44f7114310405ad","steps":[],"edges":[],"text":"A013622"},"headline":"A013622: Triangle of coefficients in expansion of (3+5x)^n.","chain":null}