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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":"A013621","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:   2,     5;\n  2:   4,    20,     25;\n  3:   8,    60,    150,    125;\n  4:  16,   160,    600,   1000,     625;\n  5:  32,   400,   2000,   5000,    6250,    3125;\n  6:  64,   960,   6000,  20000,   37500,   37500,    15625;\n  7: 128,  2240,  16800,  70000,  175000,  262500,   218750,    78125;\n  8: 256,  5120,  44800, 224000,  700000, 1400000,  1750000,  1250000,  390625;\n  9: 512, 11520, 115200, 672000, 2520000, 6300000, 10500000, 11250000, 7031250, 1953125;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (5+2*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 + 2*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 + 2*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":"A038244","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,       2;\n  2:      25,      20,        4;\n  3:     125,     150,       60,        8;\n  4:     625,    1000,      600,      160,      16;\n  5:    3125,    6250,     5000,     2000,     400,      32;\n  6:   15625,   37500,    37500,    20000,    6000,     960,     64;\n  7:   78125,  218750,   262500,   175000,   70000,   16800,   2240,    128;\n  8:  390625, 1250000,  1750000,  1400000,  700000,  224000,  44800,   5120,   256;\n  9: 1953125, 7031250, 11250000, 10500000, 6300000, 2520000, 672000, 115200, 11520, 512;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (5+2*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 + 2*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 + 2*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-01cea33b6485d9cc","steps":["basis A007318"],"edges":["e-7f6faf86ff30c5bb"],"text":"A038220 \u2192 basis A007318"},"headline":"A038220 \u2192 basis A007318","chain":null}