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48,     36,       6;\n  3:    200,    240,      90,      10;\n  4:    720,   1200,     720,     180,     15;\n  5:   2352,   5040,    4200,    1680,    315,     21;\n  6:   7168,  18816,   20160,   11200,   3360,    504,    28;\n  7:  20736,  64512,   84672,   60480,  25200,   6048,   756,    36;\n  8:  57600, 207360,  322560,  282240, 151200,  50400, 10080,  1080,   45;\n  9: 154880, 633600, 1140480, 1182720, 776160, 332640, 92400, 15840, 1485, 55;\n","recurrence_sentence":"The row polynomials satisfy (n^3-n+(3*n^2-1)*x+3*n*x^2+x^3)*P(n,x) = (8*n^3+24*n^2+16*n+(12*n^3+60*n^2+72*n+16)*x+(6*n^3+54*n^2+108*n+48)*x^2+(n^3+21*n^2+74*n+56)*x^3+(3*n^2+24*n+32)*x^4+(3*n+9)*x^5+x^6)*P(n-3,x) - (12*n^3+24*n^2-12*n-24+(12*n^3+60*n^2+36*n-36)*x+(3*n^3+42*n^2+81*n+6)*x^2+(9*n^2+48*n+33)*x^3+(9*n+18)*x^4+3*x^5)*P(n-2,x) + (6*n^3+6*n^2-12*n+(3*n^3+21*n^2+6*n-12)*x+(9*n^2+24*n)*x^2+(9*n+9)*x^3+3*x^4)*P(n-1,x) for n >= 3, with P(0,x) = 1, P(1,x) = 9 + 3*x, P(2,x) = 48 + 36*x + 6*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 9 + 3*x;\nP[2, x_] := 48 + 36*x + 6*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((8*n^3 + 24*n^2 + 16*n + (12*n^3 + 60*n^2 + 72*n + 16)*x + (6*n^3 + 54*n^2 + 108*n + 48)*x^2 + (n^3 + 21*n^2 + 74*n + 56)*x^3 + (3*n^2 + 24*n + 32)*x^4 + (3*n + 9)*x^5 + x^6)*P[n - 3, x] - (12*n^3 + 24*n^2 - 12*n - 24 + (12*n^3 + 60*n^2 + 36*n - 36)*x + (3*n^3 + 42*n^2 + 81*n + 6)*x^2 + (9*n^2 + 48*n + 33)*x^3 + (9*n + 18)*x^4 + 3*x^5)*P[n - 2, x] + (6*n^3 + 6*n^2 - 12*n + (3*n^3 + 21*n^2 + 6*n - 12)*x + (9*n^2 + 24*n)*x^2 + (9*n + 9)*x^3 + 3*x^4)*P[n - 1, x])/(n^3 - n + (3*n^2 - 1)*x + 3*n*x^2 + 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] = 9 + 3*x; v[3] = 48 + 36*x + 6*x^2; for(n = 3, N, my(i = n + 1); v[i] = ((8*n^3 + 24*n^2 + 16*n + (12*n^3 + 60*n^2 + 72*n + 16)*x + (6*n^3 + 54*n^2 + 108*n + 48)*x^2 + (n^3 + 21*n^2 + 74*n + 56)*x^3 + (3*n^2 + 24*n + 32)*x^4 + (3*n + 9)*x^5 + x^6)*v[i - 3] - (12*n^3 + 24*n^2 - 12*n - 24 + (12*n^3 + 60*n^2 + 36*n - 36)*x + (3*n^3 + 42*n^2 + 81*n + 6)*x^2 + (9*n^2 + 48*n + 33)*x^3 + (9*n + 18)*x^4 + 3*x^5)*v[i - 2] + (6*n^3 + 6*n^2 - 12*n + (3*n^3 + 21*n^2 + 6*n - 12)*x + (9*n^2 + 24*n)*x^2 + (9*n + 9)*x^3 + 3*x^4)*v[i - 1])/(n^3 - n + (3*n^2 - 1)*x + 3*n*x^2 + 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","D+1"],"edges":["e-34e3d9a08d46fb54","e-6bdd1daa8919005b"],"text":"A094305 \u2192 x \u21a6 x+1 \u2192 D+1"},"headline":"A094305 \u2192 x \u21a6 x+1 \u2192 D+1","chain":null}