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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.
3
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
0,13
FORMULA
T(n,k) = A000009(n^k).
EXAMPLE
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, ...
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 *)
PROG
(PARI) T(n, k) = polcoef(prod(j=1, n^k, 1+x^j+x*O(x^(n^k))), n^k);
CROSSREFS
Columns k=0..3 give A000012, A000009, A072243, A281501.
Rows n=0+1, 2-3 give A000012, A067735, A070235.
Main diagonal gives A064682.
Sequence in context: A128706 A375970 A253586 * A318191 A208183 A214810
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Sep 09 2021
STATUS
approved