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30,    40,    10;\n  3:   80,   180,   120,     20;\n  4:  175,   560,   630,    280,     35;\n  5:  336,  1400,  2240,   1680,    560,     56;\n  6:  588,  3024,  6300,   6720,   3780,   1008,    84;\n  7:  960,  5880, 15120,  21000,  16800,   7560,  1680,   120;\n  8: 1485, 10560, 32340,  55440,  57750,  36960, 13860,  2640,  165;\n  9: 2200, 17820, 63360, 129360, 166320, 138600, 73920, 23760, 3960, 220;\n","recurrence_sentence":"The row polynomials satisfy (n^2+n*x)*P(n,x) = (n^2+4*n+3+(n^2+5*n+6)*x+(n+3)*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((n^2 + 4*n + 3 + (n^2 + 5*n + 6)*x + (n + 3)*x^2)*P[n - 1, x])/(n^2 + n*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((n^2 + 4*n + 3 + (n^2 + 5*n + 6)*x + (n + 3)*x^2)*v[i - 1])/(n^2 + n*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-a820c1859f68e71c","steps":["D+1"],"edges":["e-f356f9ef0754fe75"],"text":"A178820 \u2192 D+1"},"headline":"A178820 \u2192 D+1","chain":null}