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 1-3 of 3 results.

A384300 a(n) = Product_{k=0..2*n-1} (3*n+k-2).

Original entry on oeis.org

1, 2, 840, 665280, 980179200, 2346549004800, 8326896754176000, 41098950018846720000, 269397128065642536960000, 2264501147602213494374400000, 23751156416080627455365283840000, 304080322557324667642345606348800000, 4667216066941750219330172809445376000000
Offset: 0

Views

Author

Seiichi Manyama, May 25 2025

Keywords

Crossrefs

Cf. A384301, A384302, A384303.
Cf. A384262.

Programs

  • PARI
    a(n) = (2*n)!*binomial(5*n-3, 2*n);

Formula

a(n) = RisingFactorial(3*n-2,2*n).
a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n-2).
a(n) = (2*n)! * binomial(5*n-3,2*n).
D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-7)*(5*n-6)*a(n-1)=0. - R. J. Mathar, May 26 2025

A384301 a(n) = Product_{k=0..2*n-1} (3*n+k-1).

Original entry on oeis.org

1, 6, 1680, 1235520, 1764322560, 4151586700800, 14572069319808000, 71382386874839040000, 465322312113382563840000, 3894941973875807210323968000, 40716268141852504209197629440000, 519879261146393786614332810854400000, 7961721525959456256504412439642112000000
Offset: 0

Views

Author

Seiichi Manyama, May 25 2025

Keywords

Crossrefs

Cf. A384300, A384302, A384303.
Cf. A384263.

Programs

  • PARI
    a(n) = (2*n)!*binomial(5*n-2, 2*n);

Formula

a(n) = RisingFactorial(3*n-1,2*n).
a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n-1).
a(n) = (2*n)! * binomial(5*n-2,2*n).
D-finite with recurrence 3*(3*n-2)*(3*n-4)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-6)*a(n-1)=0. - R. J. Mathar, May 26 2025

A384303 a(n) = Product_{k=0..2*n-1} (3*n+k+1).

Original entry on oeis.org

1, 20, 5040, 3603600, 5079110400, 11861676288000, 41430393164160000, 202250096145377280000, 1315041316842168115200000, 10985733772470225465016320000, 114660755112113373922453094400000, 1462160421974232524852811030528000000, 22368646191981329482560015901851648000000
Offset: 0

Views

Author

Seiichi Manyama, May 25 2025

Keywords

Crossrefs

Cf. A384300, A384301, A384302.
Cf. A166384.

Programs

  • PARI
    a(n) = (5*n)!/(3*n)!;

Formula

a(n) = RisingFactorial(3*n+1,2*n).
a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n+1).
a(n) = (5*n)!/(3*n)!.
D-finite with recurrence 3*(3*n-1)*(3*n-2)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, May 26 2025
Showing 1-3 of 3 results.

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

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