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 - ...)))))).

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

Author

Ilya Gutkovskiy, Aug 21 2017

Keywords

• nonn
• tabl

Examples

			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, ...
		

Crossrefs

Columns k=0-2 give A000108, A001813, A002436.

Main diagonal gives A291331.

Cf. A000079 (row 1), A063481 (row 2), A290569, A291261.

Programs

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

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.