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 A290771 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of the continued fraction 1/(1 - x/(1 - x^(2^k)/(1 - x^(3^k)/(1 - x^(4^k)/(1 - x^(5^k)/(1 - ...)))))). 3
 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 14, 1, 1, 1, 1, 3, 42, 1, 1, 1, 1, 1, 5, 132, 1, 1, 1, 1, 1, 2, 9, 429, 1, 1, 1, 1, 1, 1, 3, 15, 1430, 1, 1, 1, 1, 1, 1, 1, 4, 26, 4862, 1, 1, 1, 1, 1, 1, 1, 1, 5, 45, 16796, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 78, 58786, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 10, 135, 208012 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Table of n, a(n) for n=0..90. FORMULA G.f. of column k: 1/(1 - x/(1 - x^(2^k)/(1 - x^(3^k)/(1 - x^(4^k)/(1 - x^(5^k)/(1 - ...)))))), a continued fraction. EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, ... 2, 1, 1, 1, 1, 1, ... 5, 2, 1, 1, 1, 1, ... 14, 3, 1, 1, 1, 1, ... 42, 5, 2, 1, 1, 1, ... MATHEMATICA Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-x^(i^k), 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten CROSSREFS Columns k = 0..5 give A000108, A005169, A206739, A291146, A291149, A291168. Sequence in context: A216645 A216635 A213945 * A014651 A275422 A169951 Adjacent sequences: A290768 A290769 A290770 * A290772 A290773 A290774 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Aug 10 2017 STATUS approved

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Last modified August 10 04:12 EDT 2024. Contains 375044 sequences. (Running on oeis4.)