OFFSET
0,18
COMMENTS
In general, column k>=2 is asymptotic to k^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015
LINKS
Alois P. Heinz, Antidiagonals n = 0..43, flattened
A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz), arXiv:1108.4391 [math.CO], 2011.
FORMULA
A(n,k) = [x^(k^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, ...
0, 1, 1, 1, 1, 1, ...
0, 0, 1, 4, 7, 12, ...
0, 0, 2, 48, 310, 1240, ...
0, 0, 9, 3042, 109809, 1655004, ...
0, 0, 119, 1067474, 370702459, 32796849930, ...
MATHEMATICA
A[0, 0] = 0;
A[n_, k_] := SeriesCoefficient[Product[1/(1-x^j), {j, 1, n}], {x, 0, k^n - n(n+1)/2}];
Table[A[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Feb 16 2014
STATUS
approved