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A291260
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of continued fraction 1/(1 - 2^k*x/(1 - 4^k*x/(1 - 6^k*x/(1 - 8^k*x/(1 - 10^k*x/(1 - ...)))))).
2
1, 1, 1, 1, 2, 2, 1, 4, 12, 5, 1, 8, 80, 120, 14, 1, 16, 576, 3904, 1680, 42, 1, 32, 4352, 152064, 354560, 30240, 132, 1, 64, 33792, 6492160, 99422208, 51733504, 665280, 429, 1, 128, 266240, 290488320, 31832735744, 130292416512, 11070525440, 17297280, 1430
OFFSET
0,5
FORMULA
G.f. of column k: 1/(1 - 2^k*x/(1 - 4^k*x/(1 - 6^k*x/(1 - 8^k*x/(1 - 10^k*x/(1 - ...)))))), a continued fraction.
EXAMPLE
Square array begins:
: 1, 1, 1, 1, 1, ...
: 1, 2, 4, 8, 16, ...
: 2, 12, 80, 576, 4352, ...
: 5, 120, 3904, 152064, 6492160, ...
: 14, 1680, 354560, 99422208, 31832735744, ...
: 42, 30240, 51733504, 130292416512, 390365719822336, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i)^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 8}, {n, 0, j}] // Flatten
CROSSREFS
Columns k=0-2 give A000108, A001813, A002436.
Main diagonal gives A291331.
Cf. A000079 (row 1), A063481 (row 2), A290569, A291261.
Sequence in context: A086873 A101560 A307456 * A350825 A218529 A192456
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 21 2017
STATUS
approved