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 4624,   289;\n  9: 361, 6498, 55233, 294576, 1104660, 3093048, 6701604, 11488464, 15796638, 17551820, 15796638, 11488464, 6701604, 3093048, 1104660, 294576, 55233, 6498, 361;\n","recurrence_sentence":"The row polynomials satisfy (4*n^2-4*n+1)*P(n,x) = (4*n^2+4*n+1+(8*n^2+8*n+2)*x+(4*n^2+4*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[((4*n^2 + 4*n + 1 + (8*n^2 + 8*n + 2)*x + (4*n^2 + 4*n + 1)*x^2)*P[n - 1, x])/(4*n^2 - 4*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] = ((4*n^2 + 4*n + 1 + (8*n^2 + 8*n + 2)*x + (4*n^2 + 4*n + 1)*x^2)*v[i - 1])/(4*n^2 - 4*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)\u00b2","basis A007318"],"edges":["e-5ac7ff393747d6fc","e-a40bb3707b858dd7"],"text":"basis-map coefficients of A297191, shifted \u2192 (\u03b8+1)\u00b2 \u2192 basis A007318"},"headline":"basis-map coefficients of A297191, shifted \u2192 (\u03b8+1)\u00b2 \u2192 basis A007318","chain":null}