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(2+16*x+48*x^2+68*x^3+46*x^4+12*x^5)*d/dx P(n-1,x) for n >= 1, with P(0,x) = 13 + 42*x + 33*x^2.","mathematica":"P[0, x_] := 13 + 42*x + 33*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((9*n + 12 + (41*n + 52)*x + (67*n + 80)*x^2 + (47*n + 52)*x^3 + (12*n + 12)*x^4)*P[n - 1, x] - (2 + 16*x + 48*x^2 + 68*x^3 + 46*x^4 + 12*x^5)*D[P[n - 1, x], x])/(n + 2 + (2*n + 4)*x + (n + 2)*x^2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 13 + 42*x + 33*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((9*n + 12 + (41*n + 52)*x + (67*n + 80)*x^2 + (47*n + 52)*x^3 + (12*n + 12)*x^4)*v[i - 1] - (2 + 16*x + 48*x^2 + 68*x^3 + 46*x^4 + 12*x^5)*deriv(v[i - 1], x))/(n + 2 + (2*n + 4)*x + (n + 2)*x^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}}],"derivation":{"root":"n-b31aa1a3fd93d174","steps":["basis A007318","x \u21a6 x/(x+1)"],"edges":["e-9a0dabc7f010818b","e-799f5d25444e7556"],"text":"A133214 \u2192 basis A007318 \u2192 x \u21a6 x/(x+1)"},"headline":"A133214 \u2192 basis A007318 \u2192 x \u21a6 x/(x+1)","chain":null}