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0]"}]}],"used_by":[],"used_by_total":0,"links":[],"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:         49,          119,            71;\n  1:        343,         1372,          1757,            729;\n  2:       2401,        14749,         31066,          27559,            8842;\n  3:      16807,       158466,        496664,         710451,          480844,          125399;\n  4:     117649,      1764735,       7781641,       15952244,        17056361,         9264920,         2026249;\n  5:     823543,     20706224,     123178503,      338207261,       506704639,       429369458,       194034267,        36458010;\n  6:    5764801,    256121873,    1987326908,     6998821361,     13761622021,     16164283513,     11318595946,      4373949629,       719866701;\n  7:   40353607,   3308995774,   32702892530,   143670488171,    356196112433,    544034136079,    524900022052,    312960679507,    105588740369,     15453821461;\n  8:  282475249,  44106492451,  548549639155,  2954491807134,   8996705854962,  17171469324569,  21413749186578,  17514942881688,   9086499398956,   2718876190205,   358100141148;\n  9: 1977326743, 599977428876, 9382657517177, 61296373844069, 225076088988310, 522451377952560, 808783818830470, 850937857119329, 603402428650812, 276832502746702, 74370795456132, 8899677678109;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (7-(7*n-8)*x-(14*n+6)*x^2-(7*n+7)*x^3)*P(n-1,x) + (7*x+21*x^2+21*x^3+7*x^4)*d/dx P(n-1,x) for n >= 1, with P(0,x) = 49 + 119*x + 71*x^2.","mathematica":"P[0, x_] := 49 + 119*x + 71*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((7 - (7*n - 8)*x - (14*n + 6)*x^2 - (7*n + 7)*x^3)*P[n - 1, x] + (7*x + 21*x^2 + 21*x^3 + 7*x^4)*D[P[n - 1, x], x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 49 + 119*x + 71*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((7 - (7*n - 8)*x - (14*n + 6)*x^2 - (7*n + 7)*x^3)*v[i - 1] + (7*x + 21*x^2 + 21*x^3 + 7*x^4)*deriv(v[i - 1], x))/(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-fc18ad0ea0731402","steps":["x \u21a6 x/(x+1)"],"edges":["e-41b4eda0b54e48b3"],"text":"A075502 \u2192 x \u21a6 x/(x+1)"},"headline":"A075502 \u2192 x \u21a6 x/(x+1)","chain":null}