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45999360,     37635840,     16422912,      2985984;\n  7:   19487171,   148811124,    487018224,    885487680,    965986560,    632282112,    229920768,     35831808;\n  8:  214358881,  1870768416,   7142933952,  15584583168,  21251704320,  18546941952,  10116513792,   3153199104,   429981696;\n  9: 2357947691, 23150759148, 101021494464, 257145622272, 420783745536, 459036813312, 333844955136, 156083355648, 42568187904, 5159780352;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (11+12*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[(11 + 12*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] = (11 + 12*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":"A038337","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:         12,          11;\n  2:        144,         264,          121;\n  3:       1728,        4752,         4356,         1331;\n  4:      20736,       76032,       104544,        63888,        14641;\n  5:     248832,     1140480,      2090880,      1916640,       878460,       161051;\n  6:    2985984,    16422912,     37635840,     45999360,     31624560,     11595672,      1771561;\n  7:   35831808,   229920768,    632282112,    965986560,    885487680,    487018224,    148811124,     19487171;\n  8:  429981696,  3153199104,  10116513792,  18546941952,  21251704320,  15584583168,   7142933952,   1870768416,   214358881;\n  9: 5159780352, 42568187904, 156083355648, 333844955136, 459036813312, 420783745536, 257145622272, 101021494464, 23150759148, 2357947691;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (11+12*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[(11 + 12*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] = (11 + 12*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-9e472291b944d56e","steps":[],"edges":[],"text":"A038326"},"headline":"A038326: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*12^j.","chain":null}