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Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, ...).","first_index":0,"fingerprint":"f6-03d7b8417365c509","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["2","8"],["4","32","64"]],"card_rows":[["1"],["2","8"],["4","32","64"],["8","96","384","512"]],"row_sums_preview":["1","10","100","1000","10000","100000","1000000","10000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-ae7910bbe46f8a41","steps":["basis A013611"],"edges":["e-d7d2422771947afc"],"text":"A130123 \u2192 basis A013611"},"headline":"A130123 \u2192 basis A013611","chain":null}},{"id":"l-518ad84bd16d098f","kind":"oeis_match","node_a_id":"n-ee879560f84ab2b6","node_b_id":null,"fingerprint":null,"oeis_id":"A009964","in_catalog":0,"target":"row_sums","row_alignment":null,"rows_matched":null,"oeis_nonn":1,"details":{"alignment":{"first_row":0,"low_zeros_dropped":false,"oeis_offset":0,"oeis_term_position":2,"target":"row_sums","terms_compared":15},"in_catalog":false,"oeis_id":"A009964","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A009964","relation":"match_row_sums"}],"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:            256,            128,             16;\n  1:           4096,           3072,            768,             64;\n  2:          65536,          65536,          24576,           4096,            256;\n  3:        1048576,        1310720,         655360,         163840,          20480,          1024;\n  4:       16777216,       25165824,       15728640,        5242880,         983040,         98304,          4096;\n  5:      268435456,      469762048,      352321536,      146800640,       36700160,       5505024,        458752,        16384;\n  6:     4294967296,     8589934592,     7516192768,     3758096384,     1174405120,     234881024,      29360128,      2097152,       65536;\n  7:    68719476736,   154618822656,   154618822656,    90194313216,    33822867456,    8455716864,    1409286144,    150994944,     9437184,     262144;\n  8:  1099511627776,  2748779069440,  3092376453120,  2061584302080,   901943132160,  270582939648,   56371445760,   8053063680,   754974720,   41943040,   1048576;\n  9: 17592186044416, 48378511622144, 60473139527680, 45354854645760, 22677427322880, 7937099563008, 1984274890752, 354334801920, 44291850240, 3690987520, 184549376, 4194304;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (16+4*x)*P(n-1,x) for n >= 1, with P(0,x) = 256 + 128*x + 16*x^2.","mathematica":"P[0, x_] := 256 + 128*x + 16*x^2;\nP[n_, x_] := P[n, x] = Expand[(16 + 4*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 256 + 128*x + 16*x^2; for(n = 1, N, my(i = n + 1); v[i] = (16 + 4*x)*v[i - 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-a93042cd70c4761e","steps":["basis A007318"],"edges":["e-7b68ca495e98f7ea"],"text":"A038330 \u2192 basis A007318"},"headline":"A038330 \u2192 basis A007318","chain":null}