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v[1] = 1; v[2] = 3; for(n = 2, N, my(i = n + 1); v[i] = (2*n + 1)*v[i - 1] - (n^2 - 1 - (n^2 - 1)*x)*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":"A306364","target":"triangle","first_row":0,"oeis_offset":2,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   2:        1;\n   3:        3;\n   4:       12,         3;\n   5:       60,        45;\n   6:      360,       540,        45;\n   7:     2520,      6300,      1575;\n   8:    20160,     75600,     37800,      1575;\n   9:   181440,    952560,    793800,     99225;\n  10:  1814400,  12700800,  15876000,   3969000,   99225;\n  11: 19958400, 179625600, 314344800, 130977000, 9823275;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2*n-3)*P(n-1,x) - (n^2-4*n+3-(n^2-4*n+3)*x)*P(n-2,x) for n >= 4, with P(2,x) = 1, P(3,x) = 3.","mathematica":"P[2, x_] := 1;\nP[3, x_] := 3;\nP[n_, x_] := P[n, x] = Expand[(2*n - 3)*P[n - 1, x] - (n^2 - 4*n + 3 - (n^2 - 4*n + 3)*x)*P[n - 2, x]];\nTable[CoefficientList[P[n, x], x], {n, 2, 11}] // Flatten","pari":"P(N) = {my(v = vector(N - 1)); v[1] = 1; v[2] = 3; for(n = 4, N, my(i = n - 1); v[i] = (2*n - 3)*v[i - 1] - (n^2 - 4*n + 3 - (n^2 - 4*n + 3)*x)*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(11)","reading":{"first_row":0,"offset":2,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-3951e6b9a140d595","steps":[],"edges":[],"text":"A306364"},"headline":"A306364: Triangular array of the number of binary, rooted, leaf-labeled tree topologies with n leaves and k cherries, n >= 2, 1 <= k <= floor(n/2).","chain":null}
