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 1-8 of 8 results.

A099121 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2}.

Original entry on oeis.org

1, 3, 21, 220, 3060, 53130, 1107568, 26978328, 752538150, 23667689815, 828931106355, 32006008361808, 1350990969850340, 61902409203193230, 3060335715568296000, 162392216278033616560, 9206887338937200407418
Offset: 0

Views

Author

Sascha Kurz, Sep 28 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 2, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of a 3-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=2 of A107862 and A331436.
Cf. A099122, A099123, A099124, A099125, A099126, A099127, A099128.

Programs

  • PARI
    a(n)={binomial(binomial(n + 2, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial( (n+1)*(n+2)/2 + n-1, n).
a(n) = binomial(binomial(n + 2, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 17 2020

A331436 Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 6, 1, 0, 1, 4, 21, 20, 1, 0, 1, 5, 55, 220, 70, 1, 0, 1, 6, 120, 1540, 3060, 252, 1, 0, 1, 7, 231, 7770, 73815, 53130, 924, 1, 0, 1, 8, 406, 30856, 1088430, 5461512, 1107568, 3432, 1, 0, 1, 9, 666, 102340, 11009376, 286243776, 581106988, 26978328, 12870, 1, 0
Offset: 0

Views

Author

Andrew Howroyd, Jan 17 2020

Keywords

Examples

			Array begins:
==================================================================
n\k | 0 1   2       3         4            5              6
----+-------------------------------------------------------------
  0 | 1 1   1       1         1            1              1 ...
  1 | 0 1   2       3         4            5              6 ...
  2 | 0 1   6      21        55          120            231 ...
  3 | 0 1  20     220      1540         7770          30856 ...
  4 | 0 1  70    3060     73815      1088430       11009376 ...
  5 | 0 1 252   53130   5461512    286243776     8809549056 ...
  6 | 0 1 924 1107568 581106988 127860662755 13949678575756 ...
    ...
The A(2,2) = 6 multisets are:
   {{1,1}, {1,1}},
   {{1,1}, {1,2}},
   {{1,1}, {2,2}},
   {{1,2}, {1,2}},
   {{1,2}, {2,2}},
   {{2,2}, {2,2}}.

Links

Crossrefs

Rows n=0..3 are A000012, A001477, A002817, A140236.
Columns k=0..10 are A000007, A000012, A000984, A099121, A099122, A099123, A099124, A099125, A099126, A099127, A099128.
Min diagonal is A331477.

Programs

  • PARI
    T(n,k)={binomial(binomial(n + k - 1, n) + n - 1, n)}
{ for(n=0, 7, for(k=0, 7, print1(T(n,k), ", ")); print) }

Formula

A(n,k) = binomial(binomial(n + k - 1, n) + n - 1, n).

A099122 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3}.

Original entry on oeis.org

1, 4, 55, 1540, 73815, 5461512, 581106988, 84431259000, 16104878212995, 3910294246315600, 1178924607035010836, 432472873725488656424, 189789513537655207705620, 98222259182333060014344720
Offset: 0

Views

Author

Sascha Kurz, Sep 28 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 3, where the referees cannot be distinguished.
a(n) is the number n element multisets of n element multisets of a 4-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=4 of A331436.
Cf. A099121, A099123, A099124, A099125, A099126, A099127, A099128.

Programs

  • PARI
    a(n)={binomial(binomial(n+3, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n+3, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 17 2020

A099123 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4}.

Original entry on oeis.org

1, 5, 120, 7770, 1088430, 286243776, 127860662755, 90079147136880, 94572327271677750, 141504997346476482290, 291098519807782284023426, 799388312264077003441393875, 2859142263297618955891805452700
Offset: 0

Views

Author

Sascha Kurz, Sep 28 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 4, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of a 5-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=5 of A331436.
Cf. A099121, A099122, A099124, A099125, A099126, A099127, A099128.

Programs

  • PARI
    a(n)={binomial(binomial(n + 4, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n + 4, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 17 2020

A099124 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5}.

Original entry on oeis.org

1, 6, 231, 30856, 11009376, 8809549056, 13949678575756, 39822612151165272, 190782296093487153627, 1449479533445348118223510, 16683660613067331275158983216, 280167196060745030529247396914000, 6651137552302201488023930244802896266
Offset: 0

Views

Author

Sascha Kurz, Sep 28 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 5, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of a 6-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=6 of A331436.
Cf. A099121, A099122, A099123, A099125, A099126, A099127, A099128.

Programs

  • Mathematica
    Table[Binomial[Binomial[n+5,n]+n-1,n],{n,0,20}] (* Harvey P. Dale, Jul 26 2020 *)
  • PARI
    a(n)={binomial(binomial(n + 5, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n + 5, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended and a(12) and beyond from Andrew Howroyd, Jan 17 2020

A099126 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5,6,7}.

Original entry on oeis.org

1, 8, 666, 295240, 503167995, 2629770332904, 35773664992355004, 1119582594247762626696, 73241437035618231162682185, 9277639855710782695858431981840, 2137918570337064383107929197622033920, 850936582591338109213109187016928388683280
Offset: 0

Views

Author

Sascha Kurz, Oct 11 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 7, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of an 8-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=8 of A331436.
Cf. A099121, A099122, A099123, A099124, A099125, A099127, A099128.

Programs

  • PARI
    a(n)={binomial(binomial(n + 7, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n + 7, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended and a(11) and beyond from Andrew Howroyd, Jan 17 2020

A099127 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5,6,7,8}.

Original entry on oeis.org

1, 9, 1035, 762355, 2531986380, 29653914688398, 1023687680214527328, 90954904732217610881940, 18709083803797153776767847375, 8183604949527627465377060678018870, 7099997495119970047949715137555520213198
Offset: 0

Views

Author

Sascha Kurz, Oct 11 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 8, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of a 9-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=9 of A331436.
Cf. A099121, A099122, A099123, A099124, A099125, A099126, A099128.

Programs

  • PARI
    a(n)={binomial(binomial(n + 8, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n + 8, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended and a(10) and beyond from Andrew Howroyd, Jan 17 2020

A099128 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5,6,7,8,9}.

Original entry on oeis.org

1, 10, 1540, 1798940, 10981240985, 269343686017406, 21897427636095471460, 5097399860176368033512080, 3028721298862926523085514684685, 4186904993091626163441378607213473000, 12477686558866630120430437118910496237274716
Offset: 0

Views

Author

Sascha Kurz, Oct 11 2004

Keywords

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 9, where the referees cannot be distinguished.
a(n) is the number of n element multisets of n element multisets of a 10-set. - Andrew Howroyd, Jan 17 2020

Links

Crossrefs

Column k=10 of A331436.
Cf. A099121, A099122, A099123, A099124, A099125, A099126, A099127.

Programs

  • PARI
    a(n)={binomial(binomial(n + 9, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n + 9, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended and a(10) and beyond from Andrew Howroyd, Jan 17 2020
Showing 1-8 of 8 results.

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

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