cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A347605 Number of partitions of n^n into n or more parts.

Original entry on oeis.org

1, 1, 4, 2996, 365749566865192, 8630901377559029573671524821295260243701883575513285157821
Offset: 0

Views

Author

Seiichi Manyama, Sep 08 2021

Keywords

Comments

The next term is too large to include.

Crossrefs

Cf. A238000, A347585, A347606, A347607.

Formula

a(n) = [x^(n^n)] Sum_{k>=n} x^k / Product_{j=1..k} (1 - x^j).
a(n) = A347607(n) + A347606(n) - A238000(n).

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

Views

Author

Seiichi Manyama, Sep 08 2021

Keywords

Examples

			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.
Cf. A238016, A347615, A347617.

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).

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

Views

Author

Seiichi Manyama, Sep 08 2021

Keywords

Crossrefs

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

Formula

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).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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