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(2*n-6+(4*n-12)*x+(2*n-6)*x^2)*P(n-2,x) for n >= 4, with P(0,x) = 1, P(1,x) = 1 + x, P(2,x) = 1 + 4*x + x^2, P(3,x) = 1 + 7*x + 7*x^2 + x^3.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + x;\nP[2, x_] := 1 + 4*x + x^2;\nP[3, x_] := 1 + 7*x + 7*x^2 + x^3;\nP[n_, x_] := P[n, x] = Expand[Together[((3*n - 9 + (3*n - 9)*x)*P[n - 1, x] - (2*n - 6 + (4*n - 12)*x + (2*n - 6)*x^2)*P[n - 2, x])/(n - 3)]];\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; v[2] = 1 + x; v[3] = 1 + 4*x + x^2; v[4] = 1 + 7*x + 7*x^2 + x^3; for(n = 4, N, my(i = n + 1); v[i] = ((3*n - 9 + (3*n - 9)*x)*v[i - 1] - (2*n - 6 + (4*n - 12)*x + (2*n - 6)*x^2)*v[i - 2])/(n - 3)); 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}}],"derivation":{"root":"n-02236a48f5253afe","steps":[],"edges":[],"text":"A146986"},"headline":"A146986: Triangle, read by rows, T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + 2^(n-1) * binomial(n-2, k-1) otherwise.","chain":null}