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74256, 136136, 194480, 218790, 194480, 136136,  74256,  30940,   9520,  2040,   272,   17;\n  9: 19, 342, 2907, 15504, 58140, 162792, 352716, 604656, 831402, 923780, 831402, 604656, 352716, 162792, 58140, 15504, 2907, 342, 19;\n","recurrence_sentence":"The row polynomials satisfy (2*n-1)*P(n,x) = (2*n+1+(4*n+2)*x+(2*n+1)*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[((2*n + 1 + (4*n + 2)*x + (2*n + 1)*x^2)*P[n - 1, x])/(2*n - 1)]];\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] = ((2*n + 1 + (4*n + 2)*x + (2*n + 1)*x^2)*v[i - 1])/(2*n - 1)); 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-cdb0db4ad473ee28","steps":["\u03b8+1","x \u21a6 x+1"],"edges":["e-5ff024f1a04a7dc8","e-504cec0bc871a749"],"text":"basis-map coefficients of A297191, shifted \u2192 \u03b8+1 \u2192 x \u21a6 x+1"},"headline":"basis-map coefficients of A297191, shifted \u2192 \u03b8+1 \u2192 x \u21a6 x+1","chain":null}