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.

A216706 a(n) = Product_{k=1..n} (100 - 10/k).

Original entry on oeis.org

1, 90, 8550, 826500, 80583750, 7897207500, 776558737500, 76546504125000, 7558967282343750, 747497875698437500, 74002289694145312500, 7332954160601671875000, 727184620926332460937500, 72159089307305298046875000, 7164366724082454591796875000
Offset: 0

Views

Author

Michel Lagneau, Sep 16 2012

Keywords

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A340725.

Programs

  • Maple
    seq(product(100-10/k, k=1.. n), n=0..20);
seq((10^n/n!)*product(10*k+9, k=0.. n-1), n=0..20);

Formula

From Amiram Eldar, Aug 17 2025: (Start)
a(n) = 100^n * Gamma(n+9/10) / (Gamma(9/10) * Gamma(n+1)).
a(n) ~ c * 100^n / n^(1/10), where c = 1/Gamma(9/10) = 1/A340725 = 0.935778... . (End)

A216786 a(n) = Product_{k=1..n} (121 - 11/k).

Original entry on oeis.org

1, 110, 12705, 1490720, 176277640, 20941783632, 2495562549480, 298041470195040, 35653210872081660, 4270462368900447720, 512028438031163681628, 61443412563739641795360, 7378329792029068652259480, 886534702703800402679177520, 106574136046464005550646840440
Offset: 0

Views

Author

Michel Lagneau, Sep 16 2012

Keywords

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706.

Programs

  • Maple
    seq(product(121-11/k, k=1.. n), n=0..20);
seq((11^n/n!)*product(11*k+10, k=0.. n-1), n=0..20);
A216786 := proc(n)
    binomial(-10/11,n)*(-121)^n ;
end proc: # R. J. Mathar, Sep 17 2012
  • Mathematica
    Join[{1},FoldList[Times,121-11/Range[20]]] (* Harvey P. Dale, Mar 15 2016 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)
a(n) = 121^n * Gamma(n+10/11) / (Gamma(10/11) * Gamma(n+1)).
a(n) ~ c * 121^n / n^(1/11), where c = 1/Gamma(10/11) = 0.942148... . (End)

A216787 a(n) = Product_{k=1..n} (144 - 12/k).

Original entry on oeis.org

1, 132, 18216, 2550240, 359583840, 50917071744, 7230224187648, 1028757612985344, 146597959850411520, 20914642271992043520, 2986610916440463814656, 426813850967673556058112, 61034380688377318516310016, 8732611390798600956948971520, 1250010944797171165551838494720
Offset: 0

Views

Author

Michel Lagneau, Sep 16 2012

Keywords

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706, A216786.

Programs

  • Maple
    seq(product(144-12/k, k=1.. n), n=0..20);
seq((12^n/n!)*product(12*k+11, k=0.. n-1), n=0..20);
  • Mathematica
    Join[{1},FoldList[Times,144-12/Range[20]]] (* Harvey P. Dale, Dec 22 2015 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)
a(n) = 144^n * Gamma(n+11/12) / (Gamma(11/12) * Gamma(n+1)).
a(n) ~ c * 144^n / n^(1/12), where c = 1/Gamma(11/12) = 0.947376... . (End)

A216788 a(n) = Product_{k=1..n} (169 - 13/k).

Original entry on oeis.org

1, 156, 25350, 4174300, 691890225, 115130533440, 19207610662240, 3210414924974400, 537343198067590200, 90034838076214002400, 15098842345381088202480, 2533860269961226256525280, 425477370330989242241536600, 71480198215606192696578148800
Offset: 0

Views

Author

Michel Lagneau, Sep 16 2012

Keywords

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706, A216786, A216787.

Programs

  • Maple
    seq(product(169-13/k, k=1.. n), n=0..20);
seq((13^n/n!)*product(13*k+12, k=0.. n-1), n=0..20);
  • Mathematica
    Table[Product[169-13/k,{k,n}],{n,0,20}] (* Harvey P. Dale, Mar 13 2013 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)
a(n) = 169^n * Gamma(n+12/13) / (Gamma(12/13) * Gamma(n+1)).
a(n) ~ c * 169^n / n^(1/13), where c = 1/Gamma(12/13) = 0.951742... . (End)
Showing 1-4 of 4 results.

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