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 -11995200,     -2187360,     -176400,      -5040;\n   9:   10321920,   254217600,   1061827200,   1434343680,    813697920,    218453760,    28788480,    1774080,     40320;\n  10: -185794560, -6956772480, -40513737600, -74101910400, -56848780800, -21085868160, -4038854400, -402796800, -19595520, -362880;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(2*n-2+(n-1)*x)*P(n-1,x) - (n-1)*x*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[-(2*n - 2 + (n - 1)*x)*P[n - 1, x] - (n - 1)*x*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = -(2*n - 2 + (n - 1)*x)*v[i - 1] - (n - 1)*x*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-cf1765de6ac2bd4b","steps":["basis A008277","D+1"],"edges":["e-2b559797932c7395","e-2918bc39bdfb3040"],"text":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 D+1"},"headline":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 D+1","chain":null}