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A008288","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:          1;\n  1:         30,          18;\n  2:        525,         819,          189;\n  3:       7000,       18648,        10584,         1512;\n  4:      78750,      301266,       295974,        98658,        10206;\n  5:     787500,     3945564,      5726700,      3231900,       755244,        61236;\n  6:    7218750,    44785818,     87654798,     72611154,     28178766,      5051970,      336798;\n  7:   61875000,   457976376,   1139403672,   1274550552,    718309944,    210739320,    30600504,    1732104;\n  8:  502734375,  4323845097,  13125820851,  18762409809,  14206051431,   5993681265,  1408272723,  171694809,   8444007;\n  9: 3910156250, 38320556274, 137774943306, 241978298562, 233754090570, 131679598050, 44129631546, 8629775154, 906323418, 39405366;\n","recurrence_sentence":"The row polynomials satisfy (n^2-n)*P(n,x) = -(10*n^2+90*n+200-(3*n^2+27*n+60)*x)*P(n-2,x) + (7*n^2+28*n-35+(3*n^2+12*n-15)*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 30 + 18*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 30 + 18*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(10*n^2 + 90*n + 200 - (3*n^2 + 27*n + 60)*x)*P[n - 2, x] + (7*n^2 + 28*n - 35 + (3*n^2 + 12*n - 15)*x)*P[n - 1, x])/(n^2 - n)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 30 + 18*x; for(n = 2, N, my(i = n + 1); v[i] = (-(10*n^2 + 90*n + 200 - (3*n^2 + 27*n + 60)*x)*v[i - 2] + (7*n^2 + 28*n - 35 + (3*n^2 + 12*n - 15)*x)*v[i - 1])/(n^2 - n)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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