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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:         0;\n  1:        21,         36;\n  2:       252,       1314,         2268,          1296;\n  3:      2268,      19764,        68607,        118584,        102060,          34992;\n  4:     18144,     221616,      1156680,       3344004,       5783400,        5983632,         3429216,          839808;\n  5:    136080,    2138400,     14900760,      60429240,     157180905,      271931580,       312915960,       230947200,        99202320,         18895680;\n  6:    979776,   18825696,    164112480,     856779120,    2976375780,     7224137766,     12500778276,     15422024160,     13293110880,       7624406880,       2618941248,        408146688;\n  7:   6858432,  155784384,   1630592208,   10413549216,   45272080980,   141482532492,    327000714579,    565930129968,    733407711876,     702914572080,     484285885776,     227133631872,      64997360064,      8571080448;\n  8:  47029248, 1232838144,  15061116672,  113746114944,  593905919040,  2270917464480,   6569182774224,  14639178709512,  25338276414864,   34063761967200,   35278011590976,   27640305931392,   15859355855616,   6291173048832,   1542794480640,    176319369216;\n  9: 317447424, 9432723456, 131740680960, 1148570129664, 7001104531680, 31663079050176, 110019003684912, 299997477985968, 649909913990589, 1124990542447380, 1555983052115184, 1709806268709504, 1474432614371808, 976858895279232, 480194782099200, 165034929586176, 35407133330688, 3570467226624;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (6*n+21*n*x+18*n*x^2)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 21 + 36*x.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 21 + 36*x;\nP[n_, x_] := P[n, x] = Expand[Together[((6*n + 21*n*x + 18*n*x^2)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 21 + 36*x; for(n = 2, N, my(i = n + 1); v[i] = ((6*n + 21*n*x + 18*n*x^2)*v[i - 1])/(n - 1)); 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-eed4f744ce063213","steps":["basis A013610","D"],"edges":["e-bf76d3591eaf645b","e-9bfc12ea14b9e2ca"],"text":"A200536 \u2192 basis A013610 \u2192 D"},"headline":"A200536 \u2192 basis A013610 \u2192 D","chain":null}