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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:           169,            572,             484;\n  1:          2197,          11154,           18876,            10648;\n  2:         28561,         193336,          490776,           553696,           234256;\n  3:        371293,        3141710,        10633480,         17995120,         15226640,           5153632;\n  4:       4826809,       49010676,       207352860,        467873120,        593838960,         401983296,         113379904;\n  5:      62748517,      743328586,      3773822052,      10644113480,      18013115120,       18290239968,       10317571264,        2494357888;\n  6:     815730721,    11043738992,     65412915568,     221397560384,     468340993120,      634061652224,      536513705728,      259413220352,       54875873536;\n  7:   10604499373,   161514682758,   1093330160208,    4317252427488,   10959179239008,    18546303327552,    20924034523392,    15175673390592,     6420477203712,     1207269217792;\n  8:  137858491849,  2332989862060,  17766615103380,   80177545081920,  237448883511840,   482203886516352,   680031122010240,   657612513592320,   417331018241280,   156944998312960,   26559922791424;\n  9: 1792160394037, 33361755027458, 282291773309260, 1433173618339320, 4850741477456160, 11492525961973056, 19448890089492864, 23509647360925440, 19892778536167680, 11221567379376640, 3798068959173632, 584318301411328;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (13+35*x+22*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 169 + 572*x + 484*x^2.","mathematica":"P[0, x_] := 169 + 572*x + 484*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((13 + 35*x + 22*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 169 + 572*x + 484*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((13 + 35*x + 22*x^2)*v[i - 1])/(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-4397e742863fdbe2","steps":["basis A013610","x \u21a6 x/(x+1)"],"edges":["e-c80be26a429cc3fc","e-5e0bcdfd52348cc1"],"text":"A038305 \u2192 basis A013610 \u2192 x \u21a6 x/(x+1)"},"headline":"A038305 \u2192 basis A013610 \u2192 x \u21a6 x/(x+1)","chain":null}