OFFSET
0,8
FORMULA
G.f. of column k: Sum_{i>=0} k^(i*(i+1)/2)*x^i / Product_{j=0..i} (1 + k^j*x).
For asymptotics of column k see comment from Vaclav Kotesovec in A027880.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 16, 45, 96, 175, ...
0, 21, 416, 2835, 11904, 37625, ...
0, 315, 33280, 722925, 7428096, 48724375, ...
0, 9765, 8053760, 739552275, 23205371904, 378832015625, ...
MATHEMATICA
Table[Function[k, Product[k^j - 1, {j, 1, n}]][m - n + 1], {m, 0, 9}, {n, 0, m}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[k^(i (i + 1)/2) x^i/Product[(1 + k^j x), {j, 0, i}], {i, 0, n}], {x, 0, n}]][m - n + 1], {m, 0, 9}, {n, 0, m}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Oct 11 2018
STATUS
approved