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17965936961280, 88033091110272, 308115818885952, 770289547214880, 1348006707626040, 1572674492230380, 1100872144561266, 350277500542221;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (6+27*x+21*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 36 + 252*x + 441*x^2.","mathematica":"P[0, x_] := 36 + 252*x + 441*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((6 + 27*x + 21*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 36 + 252*x + 441*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((6 + 27*x + 21*x^2)*v[i - 1])/(1 + 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-bbfc5a54ff13a785","steps":["basis A013610","x \u21a6 x/(x+1)"],"edges":["e-46de8f4df4fd1cb3","e-3f57f2d00eaeeeb9"],"text":"A013612 \u2192 basis A013610 \u2192 x \u21a6 x/(x+1)"},"headline":"A013612 \u2192 basis A013610 \u2192 x \u21a6 x/(x+1)","chain":null}