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x]];\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] = (12 + 9*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":"A038302","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:         9,         12;\n  2:        81,        216,         144;\n  3:       729,       2916,        3888,        1728;\n  4:      6561,      34992,       69984,       62208,        20736;\n  5:     59049,     393660,     1049760,     1399680,       933120,       248832;\n  6:    531441,    4251528,    14171760,    25194240,     25194240,     13436928,      2985984;\n  7:   4782969,   44641044,   178564176,   396809280,    529079040,    423263232,    188116992,     35831808;\n  8:  43046721,  459165024,  2142770112,  5714053632,   9523422720,  10158317568,   6772211712,   2579890176,   429981696;\n  9: 387420489, 4649045868, 24794911296, 77139724032, 154279448064, 205705930752, 182849716224, 104485552128, 34828517376, 5159780352;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (12+9*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[(12 + 9*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] = (12 + 9*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":"A038335","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:         12,           9;\n  2:        144,         216,           81;\n  3:       1728,        3888,         2916,          729;\n  4:      20736,       62208,        69984,        34992,         6561;\n  5:     248832,      933120,      1399680,      1049760,       393660,        59049;\n  6:    2985984,    13436928,     25194240,     25194240,     14171760,      4251528,      531441;\n  7:   35831808,   188116992,    423263232,    529079040,    396809280,    178564176,    44641044,     4782969;\n  8:  429981696,  2579890176,   6772211712,  10158317568,   9523422720,   5714053632,  2142770112,   459165024,   43046721;\n  9: 5159780352, 34828517376, 104485552128, 182849716224, 205705930752, 154279448064, 77139724032, 24794911296, 4649045868, 387420489;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (12+9*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[(12 + 9*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] = (12 + 9*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-f485cd65a8f8089f","steps":[],"edges":[],"text":"A038335"},"headline":"A038335: Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*9^j.","chain":null}