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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":"A013628","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:      4,       5;\n  2:     16,      40,       25;\n  3:     64,     240,      300,      125;\n  4:    256,    1280,     2400,     2000,      625;\n  5:   1024,    6400,    16000,    20000,    12500,      3125;\n  6:   4096,   30720,    96000,   160000,   150000,     75000,    15625;\n  7:  16384,  143360,   537600,  1120000,  1400000,   1050000,   437500,    78125;\n  8:  65536,  655360,  2867200,  7168000, 11200000,  11200000,  7000000,  2500000,   390625;\n  9: 262144, 2949120, 14745600, 43008000, 80640000, 100800000, 84000000, 45000000, 14062500, 1953125;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (5+4*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[(5 + 4*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] = (5 + 4*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":"A038246","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:       5,        4;\n  2:      25,       40,       16;\n  3:     125,      300,      240,       64;\n  4:     625,     2000,     2400,     1280,       256;\n  5:    3125,    12500,    20000,    16000,      6400,     1024;\n  6:   15625,    75000,   150000,   160000,     96000,    30720,     4096;\n  7:   78125,   437500,  1050000,  1400000,   1120000,   537600,   143360,    16384;\n  8:  390625,  2500000,  7000000, 11200000,  11200000,  7168000,  2867200,   655360,   65536;\n  9: 1953125, 14062500, 45000000, 84000000, 100800000, 80640000, 43008000, 14745600, 2949120, 262144;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (5+4*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[(5 + 4*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] = (5 + 4*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-2e0409c0014ec240","steps":["basis A007318"],"edges":["e-13c78408b476aecd"],"text":"A013611 \u2192 basis A007318"},"headline":"A013611 \u2192 basis A007318","chain":null}