A347615
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.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 22, 30, 5, 1, 1, 1, 231, 3010, 231, 7, 1, 1, 1, 8349, 18004327, 1741630, 1958, 11, 1, 1, 1, 1741630, 133978259344888, 365749566870782, 3163127352, 17977, 15, 1, 1, 1, 4351078600, 233202632378520643600875145, 61847822068260244309086870983975, 1606903190858354689128371, 15285151248481, 173525, 22, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
1, 2, 5, 22, 231, ...
1, 3, 30, 3010, 18004327, ...
1, 5, 231, 1741630, 365749566870782, ...
Rows n=0+1, 2-10 give
A000012,
A068413,
A248728,
A068413(2*n),
A248730,
A248732,
A248734,
A068413(3*n),
A248728(2*n),
A070177.
A069878
Number of partitions of 10^n into distinct parts.
Original entry on oeis.org
1, 10, 444793, 8635565795744155161506, 1122606574548038398976040173670530159089991444775125551802871247408332723840
Offset: 0
-
Table[ PartitionsQ[10^n], {n, 0, 4}]
-
a(n) = polcoef(prod(k=1, 10^n, 1+x^k+x*O(x^(10^n))), 10^n); \\ Seiichi Manyama, Sep 10 2021
A347630
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 odd parts.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 14, 5, 1, 1, 1, 1, 23, 833, 276, 12, 1, 1, 1, 1, 276, 1731778, 2824974, 9912, 33, 1, 1, 1, 1, 11564, 1741020966255, 824068326214949, 150145281903, 602245, 93, 2, 1, 1, 1, 2824974, 78444810948209793568790, 195321031346209256918890884699755, 7375247711025022789604527681, 116880108216597935, 57638873, 276, 2, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 0, 1, 2, 5, 23, ...
1, 1, 2, 14, 833, 1731778, ...
1, 1, 5, 276, 2824974, 824068326214949, ...
1, 1, 12, 9912, 150145281903, 7375247711025022789604527681, ...
-
T(n, k) = polcoef(prod(j=0, n^k\2, 1+x^(2*j+1)+x*O(x^(n^k))), n^k);
Showing 1-3 of 3 results.