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 1-6 of 6 results.

A323546 a(n) = Product_{k=0..n} (k^8 + (n-k)^8).

Original entry on oeis.org

0, 1, 131072, 2843192875329, 94689598336441253888, 30456484467910986480712890625, 24450543078081443740165325452474318848, 74458223912158060479139869222818674648092178561, 545831702006800417886454373052629612732034857946832699392
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

Links

Crossrefs

Cf. A323538, A323540, A323541, A323542, A323543, A323544, A323545, A320345.
Cf. 2*A000542 (with sum instead of product).

Programs

  • Mathematica
    Table[Product[k^8+(n-k)^8, {k, 0, n}], {n, 0, 10}]
  • PARI
    m=8; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019
  • Sage
    m=8; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp(((2*sqrt(2+sqrt(2)) - 1/2 - sqrt(2))*Pi - 8)*n) * n^(8*n+8).

A323545 a(n) = Product_{k=0..n} (k^7 + (n-k)^7).

Original entry on oeis.org

0, 1, 32768, 79593387129, 328983774635229184, 8781626117710113525390625, 570409595340477623191338982834176, 112244673425189306235795780017831813874289, 49449149324106963036650868175987491957290049732608, 48527312221741371319651099141827554314119977393170380398241
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

Links

Crossrefs

Cf. A323535, A323540, A323541, A323542, A323543, A323544, A323546, A320345.
Cf. 2*A000541 (with sum instead of product).

Programs

  • Magma
    m:=7; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Jan 18 2019
  • Mathematica
    Table[Product[k^7+(n-k)^7, {k, 0, n}], {n, 0, 10}]
  • PARI
    m=7; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019
  • Sage
    m=7; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp((8*cos((Pi + arctan(2769*sqrt(3)/239))/6)*Pi/sqrt(21)-6)*n) * n^(7*n+7).
Equivalently, a(n) ~ exp((4*Pi*sqrt(2*(13 + 19*sin(Pi/14) - sin(3*Pi/14))/7)/7 - 6)*n) * n^(7*n+7). - Vaclav Kotesovec, Jan 23 2019

A323659 a(n) = Product_{k=0..n} (k^10 + (n-k)^10).

Original entry on oeis.org

0, 1, 2097152, 3663302861300625, 7851806399838625464320000, 378407193115560358680820465087890625, 45364420795826382440918950445637925790023680000, 34139918620704541898946466431984113559562219610081631390625
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 23 2019

Keywords

Links

Crossrefs

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323660, A323661, A323662.

Programs

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

Formula

a(n) ~ exp((Pi*(1/2 + 2*sqrt(5) - 2*sqrt(1 + 2/sqrt(5))) - 10)*n) * n^(10*n+10).

A323660 a(n) = Product_{k=0..n} (k^11 + (n-k)^11).

Original entry on oeis.org

0, 1, 8388608, 131750272043485209, 2261269183430619234140422144, 1346827225363533058227598667144775390625, 1957831179567376680040414825610884198366949236801536, 23448342360429805388842947812883850305932149345203144459397169329
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 23 2019

Keywords

Links

Crossrefs

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323661, A323662.

Programs

  • Mathematica
    Table[Product[k^11+(n-k)^11, {k, 0, n}], {n, 0, 10}]

Formula

a(n) ~ exp((2*Pi*sqrt((1225 + 504*cos(2*Pi/11) + 1512*sin(Pi/22) - 1264*sin(3*Pi/22) + 240*sin(5*Pi/22))/11)/11 - 10)*n) * n^(11*n+11).

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

Links

Crossrefs

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323660, A323662.

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

Links

Crossrefs

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323660, A323661.

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).
Showing 1-6 of 6 results.

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

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