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.

Previous Showing 11-14 of 14 results.

A323661 a(n) = Product_{k=0..n} (k^12 + (n-k)^12).

Original entry on oeis.org

0, 1, 33554432, 4740695283514005729, 651240623131512957219821846528, 4811704081770214536604871809482574462890625, 84537031377296019762303015000377965680906643309559021568, 16210797840416801857079558076889164370156937375891800497483902744790721
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 23 2019

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[k^12+(n-k)^12, {k, 0, n}], {n, 0, 10}]

Formula

a(n) ~ exp((Pi*(-5/2 + 2*sqrt(6) + sqrt(2*(5-2*sqrt(6))/3)) - 12)*n) * n^(12*n+12).

A323662 a(n) = Product_{k=0..n} (k^13 + (n-k)^13).

Original entry on oeis.org

0, 1, 134217728, 170623376651175378921, 187556828900191806607614608932864, 17233921359224498311699145473539829254150390625, 3651108402083969086976039852657366429953837378356052425179136
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 23 2019

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[k^13+(n-k)^13, {k, 0, n}], {n, 0, 10}]

Formula

a(n) ~ exp((2*Pi*sqrt((2699 - 1920*cos(2*Pi/13) + 4184*cos(3*Pi/13) - 4512*sin(Pi/26) + 4752*sin(3*Pi/26) - 2944*sin(5*Pi/26))/13) / 13 - 12)*n) * n^(13*n+13).

A376523 a(n) = Product_{k=0..n} (k^3 + n - k).

Original entry on oeis.org

0, 1, 32, 2187, 286720, 64796875, 23279477760, 12506434235113, 9582123576983552, 10084099499408154825, 14139206937856000000000, 25756714724499975610869475, 59683270195198565091221962752, 172781591936242461223503558613507, 615312169743368293769528795463680000
Offset: 0

Views

Author

Vaclav Kotesovec, Sep 26 2024

Keywords

Crossrefs

Programs

  • Maple
    A376523 := proc(n)
        mul(k^3+n-k,k=0..n) ;
    end proc:
    seq(A376523(n),n=0..20) ; # R. J. Mathar, Sep 27 2024
  • Mathematica
    Table[Product[k^3+n-k, {k, 0, n}], {n, 0, 16}]

Formula

a(n) ~ exp(2*Pi*n^(1/3)/sqrt(3) - 3*n) * n^(3*n+2) * (1 - 2*Pi/(3^(3/2)*n^(1/3)) + 2*Pi^2/(27*n^(2/3)) + (27/40 - 4*Pi^3/(243*sqrt(3)))/n).

A323751 a(n) = Product_{k=0..n} (k^n + (n-k)^n).

Original entry on oeis.org

2, 1, 32, 59049, 14101250048, 775913238525390625, 13410804447068120796679372800, 112244673425189306235795780017831813874289, 545831702006800417886454373052629612732034857946832699392
Offset: 0

Views

Author

Seiichi Manyama, Jan 26 2019

Keywords

Crossrefs

Programs

  • Magma
    [(&*[k^n +(n-k)^n: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Feb 08 2019
    
  • Mathematica
    Table[Product[k^n+(n-k)^n, {k,0,n}], {n,0,10}] (* G. C. Greubel, Feb 08 2019 *)
  • PARI
    {a(n) = prod(k=0, n, k^n+(n-k)^n)}
    
  • Sage
    [product(k^n +(n-k)^n for k in (0..n)) for n in (0..10)] # G. C. Greubel, Feb 08 2019

Formula

a(n) = n^n * A323588(n). - Vaclav Kotesovec, Feb 08 2019
Previous Showing 11-14 of 14 results.