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A347618
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 n or more parts.
2
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 4, 1, 0, 1, 1, 21, 25, 1, 0, 1, 1, 230, 2996, 201, 1, 0, 1, 1, 8348, 18004286, 1741256, 1773, 1, 0, 1, 1, 1741629, 133978259344766, 365749566865192, 3163112106, 16751, 1, 0, 1, 1, 4351078599, 233202632378520643600874780, 61847822068260244309086870896081, 1606903190858354687391986, 15285150382556, 165083, 1, 0
OFFSET
0,13
FORMULA
T(n,k) = [x^(n^k)] Sum_{i>=n} x^i / Product_{j=1..i} (1 - x^j).
T(n,k) = A347615(n,k) + A347617(n,k) - A238016(n,k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
0, 1, 4, 21, 230, ...
0, 1, 25, 2996, 18004286, ...
0, 1, 201, 1741256, 365749566865192, ...
CROSSREFS
Columns k=0..3 give A019590(n+1), A000012, A347585, A347604.
Main diagonal gives A347605.
Sequence in context: A256461 A174699 A213027 * A290459 A290458 A035253
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Sep 08 2021
STATUS
approved