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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,            650,             625;\n  1:          2197,          12675,           24375,            15625;\n  2:         28561,         219700,          633750,           812500,           390625;\n  3:        371293,        3570125,        13731250,         26406250,         25390625,           9765625;\n  4:       4826809,       55693950,       267759375,        686562500,        990234375,         761718750,         244140625;\n  5:      62748517,      844691575,      4873220625,      15619296875,      30037109375,       34658203125,       22216796875,        6103515625;\n  6:     815730721,    12549703400,     84469157500,     324881375000,     780964843750,     1201484375000,     1155273437500,      634765625000,      152587890625;\n  7:   10604499373,   183539412225,   1411841632500,    6335186812500,   18274577343750,    35143417968750,    45055664062500,    37133789062500,    17852783203125,     3814697265625;\n  8:  137858491849,  2651124843250,  22942426528125,  117653469375000,  395949175781250,   913728867187500,  1464309082031250,  1609130859375000,  1160430908203125,   495910644531250,    95367431640625;\n  9: 1792160394037, 37911085258475, 364529665946875, 2103055765078125, 8088676019531250, 21777204667968750, 41879239746093750, 57526428222656250, 55313873291015625, 35457611083984375, 13637542724609375, 2384185791015625;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (13+38*x+25*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 169 + 650*x + 625*x^2.","mathematica":"P[0, x_] := 169 + 650*x + 625*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((13 + 38*x + 25*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 + 650*x + 625*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((13 + 38*x + 25*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 A013611","x \u21a6 x/(x+1)"],"edges":["e-7b93be005ec5b750","e-30a46040fe99d754"],"text":"A038305 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)"},"headline":"A038305 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)","chain":null}