OFFSET
0,8
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
FORMULA
G.f. of column k: (1/(1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...)))))))^k, a continued fraction.
EXAMPLE
G.f. of column k: A_k(x) = 1 + k*x + k*(k + 1)*x^2/2 + k*(k^2 + 3*k + 8)*x^3/6 + k*(k^3 + 6*k^2 + 35*k + 30)*x^4/24 + ...
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 1, 3, 6, 10, 15, ...
0, 2, 6, 13, 24, 40, ...
0, 3, 11, 27, 55, 100, ...
0, 5, 20, 54, 120, 236, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-x^i, 1, {i, 1, n}])^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
Table[Function[k, SeriesCoefficient[((Sum[(-1)^i x^(i (i + 1))/Product[(1 - x^m), {m, 1, i}], {i, 0, n}])/(Sum[(-1)^i x^(i^2)/Product[(1 - x^m), {m, 1, i}], {i, 0, n}]))^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 28 2017
STATUS
approved