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 A255811 Rectangular array:  row n gives the numerators in the positive convolutory n-th root of (1,1,1,...). 2
 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 2, 1, 1, 1, 35, 14, 5, 1, 1, 1, 63, 35, 15, 3, 1, 1, 1, 231, 91, 195, 11, 7, 1, 1, 1, 429, 728, 663, 44, 91, 4, 1, 1, 1, 6435, 1976, 4641, 924, 1729, 20, 9, 1, 1, 1, 12155, 5434, 16575, 4004, 8645, 110, 51, 5, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS The convolution n times of the sequence comprising row n is the constant sequence (1,1,1,...) = A000012. It appears that if n+1 is a prime (A000040), then most of the terms in row n are divisible by n+1.  Taking n = 4 for an example, 968 of the first 1000 terms are divisible by 5. Is (column 4) = A175485, the numerators of averages of squares of 1,..,n? LINKS Clark Kimberling, Antidiagonals n = 1..60, flattened FORMULA G.f. of s:  (1 - t)^(-1/n). EXAMPLE First, regarding the numbers numerator/denominator, we have row 1:  1,1,1,1,1,1,1,1,1,1,1,1,1,..., the 0-th self-convolution of (1,1,1,...); row 2:  1,1/2,3/8,5/16,35/128,63/256, ..., convolutory sqrt of (1,1,1,...); row 3:  1,1/3,2/9,14/81,35/243,91/729,..., convolutory 3rd root; row 4:  1,1/4,5/32,15/128,195/2048,663/8192,..., convolutoary 4th root. Taking only numerators: row 1:  1,1,1,1,1,1,1,... row 2:  1,1,3,5,35,63,... row 3:  1,1,2,14,35,91,... row 4:  1,1,5,15,195,663,... MATHEMATICA z = 15; t[n_] := CoefficientList[Normal[Series[(1 - t)^(-1/n), {t, 0, z}]], t]; u = Table[Numerator[t[n]], {n, 1, z}] TableForm[Table[u[[n, k]], {n, 1, z}, {k, 1, z}]]     (* A255811 array *) Table[u[[n - k + 1, k]], {n, z}, {k, n, 1, -1}] // Flatten (* A255811 sequence *) v = Table[Denominator[t[n]], {n, 1, z}] TableForm[Table[v[[n, k]], {n, 1, z}, {k, 1, z}]]     (* A255812 array *) Table[v[[n - k + 1, k]], {n, z}, {k, n, 1, -1}] // Flatten  (* A255812 sequence *) CROSSREFS Cf. A244812, A000040, A000012. Sequence in context: A052125 A214874 A081060 * A131268 A109221 A238414 Adjacent sequences:  A255808 A255809 A255810 * A255812 A255813 A255814 KEYWORD nonn,easy,tabl,frac AUTHOR Clark Kimberling, Mar 11 2015 STATUS approved

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Last modified August 17 06:03 EDT 2017. Contains 290635 sequences.