OFFSET
0,6
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.
EXAMPLE
G.f. of column k: A_k(x) = 1 + x + (2^k + 1)*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, ...
: 2, 3, 5, 9, 17, 33, ...
: 5, 15, 61, 297, 1585, 8865, ...
: 14, 105, 1385, 24273, 485729, 10401345, ...
: 42, 945, 50521, 3976209, 372281761, 38103228225, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-i^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 9}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 08 2017
STATUS
approved