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1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+x+(2*n-2)*x^2)*P(n-1,x) + (x-x^3)*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1 + x.","mathematica":"P[1, x_] := 1 + x;\nP[n_, x_] := P[n, x] = Expand[(1 + x + (2*n - 2)*x^2)*P[n - 1, x] + (x - x^3)*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1 + x; for(n = 2, N, my(i = n); v[i] = (1 + x + (2*n - 2)*x^2)*v[i - 1] + (x - x^3)*deriv(v[i - 1], x)); 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":0,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A101842","target":"reversed_triangle","first_row":0,"oeis_offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   1: 1,    1;\n   2: 1,    3,     3,      1;\n   3: 1,    7,    16,     16,       7,        1;\n   4: 1,   15,    61,    115,     115,       61,        15,         1;\n   5: 1,   31,   206,    626,    1056,     1056,       626,       206,        31,         1;\n   6: 1,   63,   659,   2989,    7554,    11774,     11774,      7554,      2989,       659,        63,         1;\n   7: 1,  127,  2052,  13308,   47349,   105099,    154624,    154624,    105099,     47349,     13308,      2052,       127,         1;\n   8: 1,  255,  6297,  56935,  274677,   824331,   1660957,   2337507,   2337507,   1660957,    824331,    274677,     56935,      6297,      255,       1;\n   9: 1,  511, 19162, 237862, 1518478,  5960818,  15747154,  29428654,  39984640,  39984640,  29428654,  15747154,   5960818,   1518478,   237862,   19162,    511,     1;\n  10: 1, 1023, 58015, 979297, 8136844, 40851316, 137449588, 328667020, 578256262, 763546234, 763546234, 578256262, 328667020, 137449588, 40851316, 8136844, 979297, 58015, 1023, 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