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662137,   208243,    47117,     7385,     749,     43,      1;\n  8:  6561, 146529, 1102248,  4480920, 11659788,  21103740,  27841464,  27524712,  20720310,  11968614,  5308888,  1797544,   458220,   85820,  11336,    984,    49,    1;\n  9: 19683, 492075, 4192479, 19514601, 58830300, 125000172, 196501788, 235471860, 219151818, 160187338, 92459170, 42163614, 15125772, 4227132, 905004, 144516, 16491, 1251, 55, 1;\n","recurrence_sentence":"The row polynomials satisfy (3+(4*n+3)*x+(2*n+3)*x^2+x^3)*P(n,x) = (9+(12*n+33)*x+(22*n+46)*x^2+(12*n+30)*x^3+(2*n+9)*x^4+x^5)*P(n-1,x) for n >= 1, with P(0,x) = 1 + x.","mathematica":"P[0, x_] := 1 + x;\nP[n_, x_] := P[n, x] = Expand[Together[((9 + (12*n + 33)*x + (22*n + 46)*x^2 + (12*n + 30)*x^3 + (2*n + 9)*x^4 + x^5)*P[n - 1, x])/(3 + (4*n + 3)*x + (2*n + 3)*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 + x; for(n = 1, N, my(i = n + 1); v[i] = ((9 + (12*n + 33)*x + (22*n + 46)*x^2 + (12*n + 30)*x^3 + (2*n + 9)*x^4 + x^5)*v[i - 1])/(3 + (4*n + 3)*x + (2*n + 3)*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-7e353d0275e3ebc5","steps":["D+1"],"edges":["e-81a9df566ae19d38"],"text":"A299989 \u2192 D+1"},"headline":"A299989 \u2192 D+1","chain":null}