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
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 21 2017
STATUS
approved