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-46056243/268435456]"],"region_exact":{"[-1564556493/268435456, -46056243/268435456]":"[\u22123\u22122\u221a2, \u22123+2\u221a2]"},"oeis_ids":[],"derivation":{"root":"n-8d88ef9de74b305f","steps":["basis A013610","basis A008288"],"edges":["e-b88e4ed4246b1dea","e-9f3cec5348d4137f"],"text":"A038221 \u2192 basis A013610 \u2192 basis A008288"},"headline":"A038221 \u2192 basis A013610 \u2192 basis A008288","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":1,"oeis_offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   1:          1;\n   2:          5,           3;\n   3:         50,          78,           18;\n   4:        625,        1665,          945,          135;\n   5:       8750,       33474,        32886,        10962,         1134;\n   6:     131250,      657594,       954450,       538650,       125874,        10206;\n   7:    2062500,    12795948,     25044228,     20746044,      8051076,      1443420,        96228;\n   8:   33515625,   248070537,    617176989,    690381549,    389084553,    114150465,     16575273,      938223;\n   9:  558593750,  4804272330,  14584245390,  20847122010,  15784501590,   6659645850,   1564747470,   190772010,    9382230;\n  10: 9496093750, 93064208094, 334596290886, 587661582222, 567688505670, 319793309550, 107171962326, 20958025374, 2201071158, 95698746;\n","recurrence_sentence":"The row polynomials satisfy (n^2-n)*P(n,x) = -(160*n^2-640*n+600-(48*n^2-192*n+180)*x)*P(n-2,x) + (28*n^2-70*n+42+(12*n^2-30*n+18)*x)*P(n-1,x) for n >= 3, with P(1,x) = 1, P(2,x) = 5 + 3*x.","mathematica":"P[1, x_] := 1;\nP[2, x_] := 5 + 3*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(160*n^2 - 640*n + 600 - (48*n^2 - 192*n + 180)*x)*P[n - 2, x] + (28*n^2 - 70*n + 42 + (12*n^2 - 30*n + 18)*x)*P[n - 1, x])/(n^2 - n)]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; v[2] = 5 + 3*x; for(n = 3, N, my(i = n); v[i] = (-(160*n^2 - 640*n + 600 - (48*n^2 - 192*n + 180)*x)*v[i - 2] + (28*n^2 - 70*n + 42 + (12*n^2 - 30*n + 18)*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, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-a98fae1bf9eeb913","steps":["basis A013610","basis A008288"],"edges":["e-13e67b7b83b67a66","e-0c5eb7e17f6b9f42"],"text":"A085880 \u2192 basis A013610 \u2192 basis A008288"},"headline":"A085880 \u2192 basis A013610 \u2192 basis A008288","chain":null}