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  240,    180,      40;\n  4:   240,    960,   1080,     480,      75;\n  5:   672,   3360,   5040,    3360,    1050,    126;\n  6:  1792,  10752,  20160,   17920,    8400,   2016,    196;\n  7:  4608,  32256,  72576,   80640,   50400,  18144,   3528,   288;\n  8: 11520,  92160, 241920,  322560,  252000, 120960,  35280,  5760,  405;\n  9: 28160, 253440, 760320, 1182720, 1108800, 665280, 258720, 63360, 8910, 550;\n","recurrence_sentence":"The row polynomials satisfy (8+(12*n-12)*x+(6*n^2-12*n+4)*x^2+(n^3-3*n^2+2*n)*x^3)*P(n,x) = (64+(96*n+96)*x+(48*n^2+144*n+32)*x^2+(8*n^3+72*n^2+64*n-16)*x^3+(12*n^3+36*n^2-12)*x^4+(6*n^3+6*n^2-6*n-2)*x^5+(n^3-n)*x^6)*P(n-3,x) - (96+(144*n+48)*x+(72*n^2+96*n-72)*x^2+(12*n^3+60*n^2-36*n-60)*x^3+(12*n^3+6*n^2-36*n-12)*x^4+(3*n^3-3*n^2-6*n)*x^5)*P(n-2,x) + (48+(72*n-24)*x+(36*n^2-12*n-36)*x^2+(6*n^3+6*n^2-30*n+6)*x^3+(3*n^3-6*n^2-3*n+6)*x^4)*P(n-1,x) for n >= 3, with P(0,x) = 1, P(1,x) = 6 + 6*x, P(2,x) = 24 + 48*x + 18*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 6 + 6*x;\nP[2, x_] := 24 + 48*x + 18*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((64 + (96*n + 96)*x + (48*n^2 + 144*n + 32)*x^2 + (8*n^3 + 72*n^2 + 64*n - 16)*x^3 + (12*n^3 + 36*n^2 - 12)*x^4 + (6*n^3 + 6*n^2 - 6*n - 2)*x^5 + (n^3 - n)*x^6)*P[n - 3, x] - (96 + (144*n + 48)*x + (72*n^2 + 96*n - 72)*x^2 + (12*n^3 + 60*n^2 - 36*n - 60)*x^3 + (12*n^3 + 6*n^2 - 36*n - 12)*x^4 + (3*n^3 - 3*n^2 - 6*n)*x^5)*P[n - 2, x] + (48 + (72*n - 24)*x + (36*n^2 - 12*n - 36)*x^2 + (6*n^3 + 6*n^2 - 30*n + 6)*x^3 + (3*n^3 - 6*n^2 - 3*n + 6)*x^4)*P[n - 1, x])/(8 + (12*n - 12)*x + (6*n^2 - 12*n + 4)*x^2 + (n^3 - 3*n^2 + 2*n)*x^3)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 6 + 6*x; v[3] = 24 + 48*x + 18*x^2; for(n = 3, N, my(i = n + 1); v[i] = ((64 + (96*n + 96)*x + (48*n^2 + 144*n + 32)*x^2 + (8*n^3 + 72*n^2 + 64*n - 16)*x^3 + (12*n^3 + 36*n^2 - 12)*x^4 + (6*n^3 + 6*n^2 - 6*n - 2)*x^5 + (n^3 - n)*x^6)*v[i - 3] - (96 + (144*n + 48)*x + (72*n^2 + 96*n - 72)*x^2 + (12*n^3 + 60*n^2 - 36*n - 60)*x^3 + (12*n^3 + 6*n^2 - 36*n - 12)*x^4 + (3*n^3 - 3*n^2 - 6*n)*x^5)*v[i - 2] + (48 + (72*n - 24)*x + (36*n^2 - 12*n - 36)*x^2 + (6*n^3 + 6*n^2 - 30*n + 6)*x^3 + (3*n^3 - 6*n^2 - 3*n + 6)*x^4)*v[i - 1])/(8 + (12*n - 12)*x + (6*n^2 - 12*n + 4)*x^2 + (n^3 - 3*n^2 + 2*n)*x^3)); 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-7f1b09730105c8f0","steps":["x \u21a6 x+1","\u03b8+1"],"edges":["e-34e3d9a08d46fb54","e-5a40445eda7fefdf"],"text":"A094305 \u2192 x \u21a6 x+1 \u2192 \u03b8+1"},"headline":"A094305 \u2192 x \u21a6 x+1 \u2192 \u03b8+1","chain":null}