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A291261
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of continued fraction 1/(1 - x/(1 - 3^k*x/(1 - 5^k*x/(1 - 7^k*x/(1 - 9^k*x/(1 - ...)))))).
2
1, 1, 1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 10, 31, 14, 1, 1, 28, 325, 364, 42, 1, 1, 82, 4159, 22150, 5746, 132, 1, 1, 244, 57349, 1790452, 2586250, 113944, 429, 1, 1, 730, 818911, 162045118, 1691509906, 461242900, 2719291, 1430, 1, 1, 2188, 11923525, 15520964284, 1289803048426, 2978600051368, 116651486125, 75843724, 4862
OFFSET
0,6
FORMULA
G.f. of column k: 1/(1 - x/(1 - 3^k*x/(1 - 5^k*x/(1 - 7^k*x/(1 - 9^k*x/(1 - ...)))))), a continued fraction.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
2, 4, 10, 28, 82, 244, ...
5, 31, 325, 4159, 57349, 818911, ...
14, 364, 22150, 1790452, 162045118, 15520964284, ...
42, 5746, 2586250, 1691509906, 1289803048426, 1063421637466546, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i - 1)^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 9}, {n, 0, j}] // Flatten
CROSSREFS
Columns k=0..2 give A000108, A128709, A127823.
Main diagonal gives A291332.
Cf. A034472 (row 2), A290569, A291260.
Sequence in context: A363043 A192404 A373746 * A294206 A332402 A263284
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 21 2017
STATUS
approved