A347605 -id:A347605 - cp's OEIS frontend

A347606 Number of partitions of n^n into exactly n parts.

0, 1, 2, 61, 117874, 33219689231, 2559960025059106420, 85975912953927216830024650654, 1841153609473379088124269084031755459049386

Offset: 0

Seiichi Manyama, Sep 08 2021

Cf. A206240, A304176, A347605, A347607.

a(n) = polcoef(prod(k=1, n, 1/(1-x^k+x*O(x^(n^n-n)))), n^n-n);

a(n) = [x^(n^n-n)] Product_{k=1..n} 1/(1-x^k).

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.

Original entry on oeis.org

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

Seiichi Manyama, Sep 08 2021

			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, ...

Columns k=0..3 give A019590(n+1), A000012, A347585, A347604.
Main diagonal gives A347605.
Cf. A238016, A347615, A347617.

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).

A347604 Number of partitions of n^3 into n or more parts.

Original entry on oeis.org

1, 1, 21, 2996, 1741256, 3163112106, 15285150382556, 175943559746571618, 4453575699565108152534, 233202632378520005314974035, 24061467864032622392081524591073, 4700541557913558825449308701662220085, 1681375219875327721201831964319709743701981

Offset: 0

Seiichi Manyama, Sep 08 2021

nonn

Cf. A128854, A238608, A304176, A347585, A347605.

a(n) = [x^(n^3)] Sum_{k>=n} x^k / Product_{j=1..k} (1 - x^j).

a(n) = A128854(n) + A304176(n) - A238608(n).

cp's OEIS Frontend

A347606 Number of partitions of n^n into exactly n parts.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

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.

Views

Author

Keywords

Examples

Crossrefs

Formula

A347604 Number of partitions of n^3 into n or more parts.

Views

Author

Keywords

Crossrefs

Formula