A347621 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is the number of partitions of n^k into distinct parts.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 6, 8, 2, 1, 1, 1, 32, 192, 32, 3, 1, 1, 1, 390, 84756, 16444, 142, 4, 1, 1, 1, 16444, 5807301632, 11784471548, 3207086, 668, 5, 1, 1, 1, 4013544, 2496696209705056142, 16816734263788624008200, 74443865946867656, 1258238720, 3264, 6, 1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, ... 1, 1, 2, 6, 32, ... 1, 2, 8, 192, 84756, ... 1, 2, 32, 16444, 11784471548, ...
Crossrefs
Programs
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Mathematica
Table[If[n == k == 0, 1, PartitionsQ[#^k] &[n - k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten (* Michael De Vlieger, Sep 09 2021 *) -
PARI
T(n, k) = polcoef(prod(j=1, n^k, 1+x^j+x*O(x^(n^k))), n^k);
Formula
T(n,k) = A000009(n^k).
Comments