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92,   33,     2;\n   6: 2, 41, 200,  200,    41,     2;\n   7: 2, 49, 340,  676,   340,    49,    2;\n   8: 2, 57, 512, 1616,  1616,   512,   57,   2;\n   9: 2, 65, 716, 3148,  5260,  3148,  716,  65,  2;\n  10: 2, 73, 952, 5400, 13256, 13256, 5400, 952, 73, 2;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (n-3)*P(n,x) = (n-3+(n-3)*x)*P(n-1,x) + (3*n-9)*x*P(n-2,x) for n >= 4, with P(1,x) = 2, P(2,x) = 3 + 3*x, P(3,x) = 2 + 14*x + 2*x^2.","mathematica":"P[1, x_] := 2;\nP[2, x_] := 3 + 3*x;\nP[3, x_] := 2 + 14*x + 2*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 3 + (n - 3)*x)*P[n - 1, x] + (3*n - 9)*x*P[n - 2, x])/(n - 3)]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n]], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 2; v[2] = 3 + 3*x; v[3] = 2 + 14*x + 2*x^2; for(n = 4, N, my(i = n); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1] + (3*n - 9)*x*v[i - 2])/(n - 3)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":0,"offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-71548025909043e7","steps":[],"edges":[],"text":"A153516"},"headline":"A153516: Triangle T(n,k,p,q,j) = T(n-1,k,p,q,j) + T(n-1,k-1,p,q,j) + (p*j+q)*prime(j)*T(n-2,k-1,p,q,j) with T(2,k,p,q,j) = prime(j) and (p,q,j) = (0,1,2), read by rows.","chain":null}