A291207 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 - 2^k*x/(1 + 3^k*x/(1 - 4^k*x/(1 + 5^k*x/(1 - ...)))))).

1, 1, -1, 1, -1, 0, 1, -1, -1, 1, 1, -1, -3, 5, 0, 1, -1, -7, 27, 17, -2, 1, -1, -15, 167, 441, -121, 0, 1, -1, -31, 1071, 10673, -11529, -721, 5, 1, -1, -63, 6815, 262305, -1337713, -442827, 6845, 0, 1, -1, -127, 42687, 6525377, -161721441, -297209047, 23444883, 58337, -14

Offset: 0

Author

Ilya Gutkovskiy, Aug 21 2017

Keywords

• sign
• tabl

Examples

			G.f. of column k: A_k(x) = 1 - x + (1 - 2^k)*x^2 + (2^(k + 1) - 4^k + 6^k - 1)*x^3 + ...
Square array begins:
   1,     1,       1,         1,           1,             1,  ...
  -1,    -1,      -1,        -1,          -1,            -1,  ...
   0,    -1,      -3,        -7,         -15,           -31,  ...
   1,     5,      27,       167,        1071,          6815,  ...
   0,    17,     441,     10673,      262305,       6525377,  ...
  -2,  -121,  -11529,  -1337713,  -161721441,  -19802585281,  ...
		

Crossrefs

Columns k=0-2 give A105523, A202038, A193544.

Main diagonal gives A292920.

Cf. A290569.

Programs

Mathematica

Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(-1)^i i^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 9}, {n, 0, j}] // Flatten

Formula

G.f. of column k: 1/(1 + x/(1 - 2^k*x/(1 + 3^k*x/(1 - 4^k*x/(1 + 5^k*x/(1 - ...)))))), a continued fraction.