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begins:\n  0:      1;\n  1:      4,      1;\n  2:     15,      8,      1;\n  3:     56,     46,     12,      1;\n  4:    209,    232,     93,     16,      1;\n  5:    780,   1091,    592,    156,     20,     1;\n  6:   2911,   4912,   3366,   1200,    235,    24,    1;\n  7:  10864,  21468,  17784,   8010,   2120,   330,   28,   1;\n  8:  40545,  91824,  89238,  48624,  16255,  3416,  441,  32,  1;\n  9: 151316, 386373, 430992, 275724, 111524, 29589, 5152, 568, 36, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4+x)*P(n-1,x) - P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 4 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 4 + x;\nP[n_, x_] := P[n, x] = Expand[(4 + x)*P[n - 1, x] - P[n - 2, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 4 + x; for(n = 2, N, my(i = n + 1); v[i] = (4 + x)*v[i - 1] - v[i - 2]); 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":"A207823","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:      4,      1;\n  2:     15,      8,      1;\n  3:     56,     46,     12,      1;\n  4:    209,    232,     93,     16,      1;\n  5:    780,   1091,    592,    156,     20,     1;\n  6:   2911,   4912,   3366,   1200,    235,    24,    1;\n  7:  10864,  21468,  17784,   8010,   2120,   330,   28,   1;\n  8:  40545,  91824,  89238,  48624,  16255,  3416,  441,  32,  1;\n  9: 151316, 386373, 430992, 275724, 111524, 29589, 5152, 568, 36, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4+x)*P(n-1,x) - P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 4 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 4 + x;\nP[n_, x_] := P[n, x] = Expand[(4 + x)*P[n - 1, x] - P[n - 2, 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; v[2] = 4 + x; for(n = 2, N, my(i = n + 1); v[i] = (4 + x)*v[i - 1] - v[i - 2]); 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-30cb3cad216ed189","steps":[],"edges":[],"text":"A207823"},"headline":"A207823: Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).","chain":null}