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3069402336000,      1002550348800,        87178291200;\n  8:   1212135593793,   29265860447536,   222494217046944,    794354143040640,   1533871279100160,   1669219346995200,    989822318284800,    275483400192000,    20922789888000;\n  9: 186388033956483, 5532759960522002, 52101046426636320, 234537391905814080, 588855455629459200, 876964309110489600, 779061750321254400, 391736348933529600, 94968543301632000, 6402373705728000;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(3-4*x-22*x^2-16*x^3+8*x^4)*P(n-2,x) + (6+40*x+138*x^2+156*x^3+12*x^4-40*x^5)*d/dx P(n-2,x) + (4*x+32*x^2+60*x^3+24*x^4-24*x^5-16*x^6)*d^2/dx^2 P(n-2,x) + (8-14*x^2+4*x^3)*P(n-1,x) + (6+28*x+22*x^2)*d/dx P(n-1,x) + (4*x+8*x^2+4*x^3)*d^2/dx^2 P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 3 + 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + 2*x;\nP[n_, x_] := P[n, x] = Expand[-(3 - 4*x - 22*x^2 - 16*x^3 + 8*x^4)*P[n - 2, x] + (6 + 40*x + 138*x^2 + 156*x^3 + 12*x^4 - 40*x^5)*D[P[n - 2, x], x] + (4*x + 32*x^2 + 60*x^3 + 24*x^4 - 24*x^5 - 16*x^6)*D[P[n - 2, x], {x, 2}] + (8 - 14*x^2 + 4*x^3)*P[n - 1, x] + (6 + 28*x + 22*x^2)*D[P[n - 1, x], x] + (4*x + 8*x^2 + 4*x^3)*D[P[n - 1, x], {x, 2}]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3 + 2*x; for(n = 2, N, my(i = n + 1); v[i] = -(3 - 4*x - 22*x^2 - 16*x^3 + 8*x^4)*v[i - 2] + (6 + 40*x + 138*x^2 + 156*x^3 + 12*x^4 - 40*x^5)*deriv(v[i - 2], x) + (4*x + 32*x^2 + 60*x^3 + 24*x^4 - 24*x^5 - 16*x^6)*deriv(deriv(v[i - 2], x), x) + (8 - 14*x^2 + 4*x^3)*v[i - 1] + (6 + 28*x + 22*x^2)*deriv(v[i - 1], x) + (4*x + 8*x^2 + 4*x^3)*deriv(deriv(v[i - 1], x), 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-3338feb205e3b77f","steps":["D+1"],"edges":["e-b9e177303601478a"],"text":"A151775 \u2192 D+1"},"headline":"A151775 \u2192 D+1","chain":null}