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polynomials satisfy (n+n^2*x)*P(n,x) = (n+5+(n^2+7*n+10)*x+(n^2+6*n+5)*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((n + 5 + (n^2 + 7*n + 10)*x + (n^2 + 6*n + 5)*x^2)*P[n - 1, x])/(n + n^2*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((n + 5 + (n^2 + 7*n + 10)*x + (n^2 + 6*n + 5)*x^2)*v[i - 1])/(n + n^2*x)); 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-97228a88c81561dc","steps":["\u03b8+1"],"edges":["e-d8e82314ed3cc2a2"],"text":"A178822 \u2192 \u03b8+1"},"headline":"A178822 \u2192 \u03b8+1","chain":null}