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38737416,  206181928,  435737144,  406365720,  172600120,   32865464,   2600712,    65536;\n  9: 11430696, 276815832, 1997698544, 5860802152, 7858765776, 5039544104, 1551390448, 222172056, 13527848, 262144;\n","recurrence_sentence":"The row polynomials satisfy (n+1+2*x)*P(n,x) = -(20*n+40+(8*n^2+20*n+48)*x+(n^3+4*n^2+24*n+16)*x^2+(3*n^2+8*n+12)*x^3+(2*n+4)*x^4)*P(n-2,x) - ((4*n+8)*x+(n^2-n+2)*x^2-(n^2+6)*x^3-(3*n+2)*x^4-2*x^5)*d/dx P(n-2,x) + (9*n+13+(2*n^2+5*n+21)*x+(5*n+6)*x^2+2*x^3)*P(n-1,x) + ((n+1)*x-(n-1)*x^2-2*x^3)*d/dx P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 8 + 4*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 8 + 4*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(20*n + 40 + (8*n^2 + 20*n + 48)*x + (n^3 + 4*n^2 + 24*n + 16)*x^2 + (3*n^2 + 8*n + 12)*x^3 + (2*n + 4)*x^4)*P[n - 2, x] - ((4*n + 8)*x + (n^2 - n + 2)*x^2 - (n^2 + 6)*x^3 - (3*n + 2)*x^4 - 2*x^5)*D[P[n - 2, x], x] + (9*n + 13 + (2*n^2 + 5*n + 21)*x + (5*n + 6)*x^2 + 2*x^3)*P[n - 1, x] + ((n + 1)*x - (n - 1)*x^2 - 2*x^3)*D[P[n - 1, x], x])/(n + 1 + 2*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 8 + 4*x; for(n = 2, N, my(i = n + 1); v[i] = (-(20*n + 40 + (8*n^2 + 20*n + 48)*x + (n^3 + 4*n^2 + 24*n + 16)*x^2 + (3*n^2 + 8*n + 12)*x^3 + (2*n + 4)*x^4)*v[i - 2] - ((4*n + 8)*x + (n^2 - n + 2)*x^2 - (n^2 + 6)*x^3 - (3*n + 2)*x^4 - 2*x^5)*deriv(v[i - 2], x) + (9*n + 13 + (2*n^2 + 5*n + 21)*x + (5*n + 6)*x^2 + 2*x^3)*v[i - 1] + ((n + 1)*x - (n - 1)*x^2 - 2*x^3)*deriv(v[i - 1], x))/(n + 1 + 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-c47b645304a2946e","steps":["D+1"],"edges":["e-178736c321ffb562"],"text":"A257606 \u2192 D+1"},"headline":"A257606 \u2192 D+1","chain":null}