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 1;\n   5: 1,    76,     230,       76,        1;\n   6: 1,   237,    1682,     1682,      237,        1;\n   7: 1,   722,   10543,    23548,    10543,      722,        1;\n   8: 1,  2179,   60657,   259723,   259723,    60657,     2179,       1;\n   9: 1,  6552,  331612,  2485288,  4675014,  2485288,   331612,    6552,     1;\n  10: 1, 19673, 1756340, 21707972, 69413294, 69413294, 21707972, 1756340, 19673, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (1+(2*n-3)*x)*P(n-1,x) + (2*x-2*x^2)*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(1 + (2*n - 3)*x)*P[n - 1, x] + (2*x - 2*x^2)*D[P[n - 1, x], x]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n]], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = (1 + (2*n - 3)*x)*v[i - 1] + (2*x - 2*x^2)*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-1be5eefbe5bc79ec","steps":[],"edges":[],"text":"A060187"},"headline":"A060187: Triangle read by rows: Eulerian numbers of type B, T(n,k) (1 <= k <= n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (2*n - 2*k + 1)*T(n-1, k-1) + (2*k - 1)*T(n-1, k).","chain":null}