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binomial(i,j)*11^(i-j)*5^j.","first_index":0,"fingerprint":"f6-833b492313a93e6e","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["256","160","25"],["4096","3840","1200","125"],["65536","81920","38400","8000","625"]],"card_rows":[["256","160","25"],["4096","3840","1200","125"],["65536","81920","38400","8000","625"],["1048576","1638400","1024000","320000","50000","3125"]],"row_sums_preview":["441","9261","194481","4084101","85766121","1801088541","37822859361","794280046581"],"regions":["(-inf, 0]","(-inf, -1]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-2bc1923905556bf6","steps":["x \u21a6 x+1"],"edges":["e-2406b2ec50933490"],"text":"A038319 \u2192 x \u21a6 x+1"},"headline":"A038319 \u2192 x \u21a6 x+1","chain":null}}],"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:             400,             2560,               4096;\n  1:            8000,            76800,             245760,              262144;\n  2:          160000,          2048000,            9830400,            20971520,            16777216;\n  3:         3200000,         51200000,          327680000,          1048576000,          1677721600,           1073741824;\n  4:        64000000,       1228800000,         9830400000,         41943040000,        100663296000,         128849018880,           68719476736;\n  5:      1280000000,      28672000000,       275251200000,       1468006400000,       4697620480000,        9019431321600,         9620726743040,         4398046511104;\n  6:     25600000000,     655360000000,      7340032000000,      46976204800000,     187904819200000,      481036337152000,       769658139443200,       703687441776640,       281474976710656;\n  7:    512000000000,   14745600000000,    188743680000000,    1409286144000000,    6764573491200000,    21646635171840000,     46179488366592000,     63331869759897600,     50665495807918080,     18014398509481984;\n  8:  10240000000000,  327680000000000,   4718592000000000,   40265318400000000,  225485783040000000,   865865406873600000,   2308974418329600000,   4222124650659840000,   5066549580791808000,   3602879701896396800,   1152921504606846976;\n  9: 204800000000000, 7208960000000000, 115343360000000000, 1107296256000000000, 7086696038400000000, 31748398252032000000, 101594874406502400000, 232216855786291200000, 371546969258065920000, 396316767208603648000, 253642731013506334720, 73786976294838206464;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (20+84*x+64*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 400 + 2560*x + 4096*x^2.","mathematica":"P[0, x_] := 400 + 2560*x + 4096*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((20 + 84*x + 64*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] = 400 + 2560*x + 4096*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((20 + 84*x + 64*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-cfc5b48d32898a3e","steps":["basis A013611","x \u21a6 x/(x+1)"],"edges":["e-9ac6ce8d07a161c9","e-a514a8c4e4bac18f"],"text":"A038301 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)"},"headline":"A038301 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)","chain":null}