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 1-4 of 4 results.

A272244 a(n) = Product_{k=0..n} (n^2 + k^2).

Original entry on oeis.org

0, 2, 160, 21060, 4352000, 1313845000, 547573478400, 301758856490000, 212663770808320000, 186659516597629140000, 199722414913149440000000, 255947740845844788169000000, 387074162712817024892928000000, 682170272459193898736228210000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[n^2+k^2,{k,0,n}],{n,0,15}]

Formula

a(n) ~ 2^(n + 1/2) * n^(2*(n+1)) / exp((4-Pi)*n/2).

A272238 a(n) = Product_{k=0..n} (n^2+k)!.

Original entry on oeis.org

1, 2, 2073600, 25177856146146034974720000000, 14100949826093501607549529280892932893801777581548587107609477120000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Comments

The next term has 173 digits.

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2+k)!, {k, 0, n}], {n, 0, 6}]
    Table[BarnesG[n^2 + n + 2]/BarnesG[n^2 + 1], {n, 0, 6}]

Formula

a(n) = ((n^2+n)!)^(n+1) / A272237(n).
a(n) ~ exp(11/24 + n/6 - n^2 - n^3) * n^((1+n)*(1 + n + 2*n^2)) * (2*Pi)^((n+1)/2).

A272179 a(n) = Product_{k=0..n} (n^2 - k).

Original entry on oeis.org

0, 0, 24, 3024, 524160, 127512000, 42072307200, 18183435621120, 9993927307714560, 6816310367682816000, 5653408585997652480000, 5606015030436835542528000, 6551662594343454506664345600, 8914054345090074511550572953600, 13970892529731225585461744812032000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[n^2 - k, {k, 0, n}], {n, 0, 15}]
    Table[(n-1)*n*Pochhammer[1 - n + n^2, n], {n, 0, 15}]

Formula

a(n) ~ exp(-1/2) * n^(2*n + 2).

A272237 a(n) = Product_{k=0..n} (n^2+k)^k.

Original entry on oeis.org

2, 180, 2090880, 6044699520000, 7151106328088486400000, 5159620144413185246982598164480000, 3167269298042065159436486399933762922086400000000, 2200712918907364598767850489247066133407004510957047455416320000000
Offset: 1

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2+k)^k, {k, 0, n}], {n, 1, 10}]
    Table[((n^2+n)!)^(n+1) * BarnesG[n^2 + 1] / BarnesG[n^2 + n + 2], {n, 1, 10}]

Formula

a(n) = ((n^2+n)!)^(n+1) / A272238(n).
a(n) ~ exp(n/3 + 3/8) * n^(n*(n+1)).
Showing 1-4 of 4 results.