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-402605562240, -566015869440, -472633418880, -216695606400, -42085008000;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = -(n-1-(n^2-6*n+5)*x-(2*n^2-8*n+6)*x^2-(n^2-3*n+2)*x^3)*P(n-1,x) - ((n-1)*x+(3*n-3)*x^2+(3*n-3)*x^3+(n-1)*x^4)*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[Together[(-(n - 1 - (n^2 - 6*n + 5)*x - (2*n^2 - 8*n + 6)*x^2 - (n^2 - 3*n + 2)*x^3)*P[n - 1, x] - ((n - 1)*x + (3*n - 3)*x^2 + (3*n - 3)*x^3 + (n - 1)*x^4)*D[P[n - 1, x], x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = (-(n - 1 - (n^2 - 6*n + 5)*x - (2*n^2 - 8*n + 6)*x^2 - (n^2 - 3*n + 2)*x^3)*v[i - 1] - ((n - 1)*x + (3*n - 3)*x^2 + (3*n - 3)*x^3 + (n - 1)*x^4)*deriv(v[i - 1], x))/(1 + x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-cf1765de6ac2bd4b","steps":["basis A008277","x \u21a6 x/(x+1)"],"edges":["e-2b559797932c7395","e-0bdf5da5ae839b0b"],"text":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 x \u21a6 x/(x+1)"},"headline":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 x \u21a6 x/(x+1)","chain":null}