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450,    10;\n   9: 11, 11253,  313511, 1603250,  2714030,  1974357,  703857,  130680,  12705,   605,  11;\n  10: 12, 24564, 1038312, 7338012, 16552800, 15883824, 7528752, 1908324, 267300, 20460, 792, 12;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (n+2+(n+2)*x)*P(n-1,x) + (n+2)*x*d/dx P(n-1,x) for n >= 2, with P(1,x) = 3 + 9*x + 3*x^2.","mathematica":"P[1, x_] := 3 + 9*x + 3*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n + 2 + (n + 2)*x)*P[n - 1, x] + (n + 2)*x*D[P[n - 1, x], x])/(n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 3 + 9*x + 3*x^2; for(n = 2, N, my(i = n); v[i] = ((n + 2 + (n + 2)*x)*v[i - 1] + (n + 2)*x*deriv(v[i - 1], x))/(n + 1)); 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-5fe240122e98ffb3","steps":["\u03b8+1","basis A008277"],"edges":["e-972f6eabe8338070","e-cc01c1bc9ab032b7"],"text":"basis-map coefficients of A112227 \u2192 \u03b8+1 \u2192 basis A008277"},"headline":"basis-map coefficients of A112227 \u2192 \u03b8+1 \u2192 basis A008277","chain":null}