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 - ...)))))).

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

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