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-46056243/268435456]"],"region_exact":{"[-1564556493/268435456, -46056243/268435456]":"[\u22123\u22122\u221a2, \u22123+2\u221a2]"},"oeis_ids":[],"derivation":{"root":"n-97228a88c81561dc","steps":["basis A013610","basis A008288"],"edges":["e-3fa86ece9d0bedd1","e-31efb735b14ec404"],"text":"A178822 \u2192 basis A013610 \u2192 basis A008288"},"headline":"A178822 \u2192 basis A013610 \u2192 basis 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:        20,         12;\n  2:       250,        390,          90;\n  3:      2500,       6660,        3780,         540;\n  4:     21875,      83685,       82215,       27405,        2835;\n  5:    175000,     876792,     1272600,      718200,      167832,       13608;\n  6:   1312500,    8142876,    15937236,    13202028,     5123412,      918540,      61236;\n  7:   9375000,   69390360,   172636920,   193113720,   108834840,    31930200,    4636440,    262440;\n  8:  64453125,  554339115,  1682797545,  2405437155,  1821288645,   768420675,  180547785,  22012155,  1082565;\n  9: 429687500, 4211050140, 15140103660, 26591021820, 25687262700, 14470285500, 4849410060, 948326940, 99595980, 4330260;\n","recurrence_sentence":"The row polynomials satisfy (n^2-n)*P(n,x) = -(10*n^2+50*n+60-(3*n^2+15*n+18)*x)*P(n-2,x) + (7*n^2+14*n-21+(3*n^2+6*n-9)*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 20 + 12*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 20 + 12*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(10*n^2 + 50*n + 60 - (3*n^2 + 15*n + 18)*x)*P[n - 2, x] + (7*n^2 + 14*n - 21 + (3*n^2 + 6*n - 9)*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] = 20 + 12*x; for(n = 2, N, my(i = n + 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