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 1-5 of 5 results.

A347607 Number of partitions of n^n.

Original entry on oeis.org

1, 1, 5, 3010, 365749566870782, 8630901377559029573671524821295260243701883575513498104067
Offset: 0

Views

Author

Seiichi Manyama, Sep 08 2021

Keywords

Comments

The next term a(6) = 1.30449952...*10^235 is too large to include.
a(7) = 1.5782589391...*10^1004. - Chai Wah Wu, Sep 09 2021

Crossrefs

Main diagonal of A347615.

Programs

  • Maple
    a:= n-> combinat[numbpart](n^n):
    seq(a(n), n=0..6);  # Alois P. Heinz, Sep 09 2021
  • PARI
    a(n) = numbpart(n^n);
    
  • Python
    from sympy.functions import partition
    def A347607(n): return partition(n**n) # Chai Wah Wu, Sep 09 2021

Formula

a(n) = A000041(n^n).

A069878 Number of partitions of 10^n into distinct parts.

Original entry on oeis.org

1, 10, 444793, 8635565795744155161506, 1122606574548038398976040173670530159089991444775125551802871247408332723840
Offset: 0

Views

Author

Robert G. Wilson v, May 03 2002

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ PartitionsQ[10^n], {n, 0, 4}]
  • PARI
    a(n) = polcoef(prod(k=1, 10^n, 1+x^k+x*O(x^(10^n))), 10^n); \\ Seiichi Manyama, Sep 10 2021

Formula

a(n) = A000009(A011557(n)). - Michel Marcus, Sep 10 2021

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.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Sep 09 2021

Keywords

Examples

			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, ...
		

Crossrefs

Columns k=0..3 give A000012, A000009, A072243, A281501.
Rows n=0+1, 2-3 give A000012, A067735, A070235.
Main diagonal gives A064682.

Programs

  • 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 *)
  • PARI
    T(n, k) = polcoef(prod(j=1, n^k, 1+x^j+x*O(x^(n^k))), n^k);

Formula

T(n,k) = A000009(n^k).

A347626 Number of partitions of n^n into distinct odd parts.

Original entry on oeis.org

1, 1, 1, 14, 2824974, 7375247711025022789604527681
Offset: 0

Views

Author

Seiichi Manyama, Sep 09 2021

Keywords

Comments

The next term a(6) = 1.46058224...*10^116 is too large to include.

Crossrefs

Main diagonal of A347630.

Programs

  • PARI
    a(n) = polcoef(prod(k=0, n^n\2, 1+x^(2*k+1)+x*O(x^(n^n))), n^n);

Formula

a(n) = [x^(n^n)] Product_{k>=0} (1 + x^(2*k+1)).
a(n) = A000700(n^n).

A152425 Integer part of the n-th root of the number of partitions of n^n into distinct parts.

Original entry on oeis.org

1, 1, 5, 329, 137483613, 4509583237978309488810051189, 242639939633545703354650791456741100816768201372832720247783531678176442265132915735721710004729333425
Offset: 1

Views

Author

Keywords

Crossrefs

Cf. A064682.

Programs

  • Mathematica
    Table[IntegerPart[PartitionsQ[n^n]^(1/n)],{n,1,7}]

Extensions

Definition amended and a(7) from Georg Fischer, Oct 24 2024
Showing 1-5 of 5 results.