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5*x)*v[i - 1]); 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}},{"oeis_id":"A038248","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,        6;\n  2:      25,       60,        36;\n  3:     125,      450,       540,       216;\n  4:     625,     3000,      5400,      4320,      1296;\n  5:    3125,    18750,     45000,     54000,     32400,      7776;\n  6:   15625,   112500,    337500,    540000,    486000,    233280,     46656;\n  7:   78125,   656250,   2362500,   4725000,   5670000,   4082400,   1632960,    279936;\n  8:  390625,  3750000,  15750000,  37800000,  56700000,  54432000,  32659200,  11197440,  1679616;\n  9: 1953125, 21093750, 101250000, 283500000, 510300000, 612360000, 489888000, 251942400, 75582720, 10077696;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (6+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[(6 + 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] = (6 + 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}},{"oeis_id":"A038259","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:        6,        5;\n  2:       36,       60,        25;\n  3:      216,      540,       450,       125;\n  4:     1296,     4320,      5400,      3000,       625;\n  5:     7776,    32400,     54000,     45000,     18750,      3125;\n  6:    46656,   233280,    486000,    540000,    337500,    112500,     15625;\n  7:   279936,  1632960,   4082400,   5670000,   4725000,   2362500,    656250,     78125;\n  8:  1679616, 11197440,  32659200,  54432000,  56700000,  37800000,  15750000,   3750000,   390625;\n  9: 10077696, 75582720, 251942400, 489888000, 612360000, 510300000, 283500000, 101250000, 21093750, 1953125;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (6+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[(6 + 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] = (6 + 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}}],"derivation":{"root":"n-e6ebe74518d42cbe","steps":[],"edges":[],"text":"A038259"},"headline":"A038259: Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j)*5^j.","chain":null}