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 1-2 of 2 results.

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

A384262 a(n) = Product_{k=0..n-1} (3*n+k-2).

Original entry on oeis.org

1, 1, 20, 504, 17160, 742560, 39070080, 2422728000, 173059286400, 13995229248000, 1264020397516800, 126115611484262400, 13776096431889792000, 1635195634511530291200, 209574860127295703040000, 28844656968251942737920000, 4243193364951971128258560000, 664387519844376163893657600000
Offset: 0

Views

Author

Seiichi Manyama, May 23 2025

Keywords

Crossrefs

Cf. A061924, A384164, A384263.
Cf. A335647.

Programs

  • PARI
    a(n) = prod(k=0, n-1, 3*n+k-2);
  • Python
    from sympy import rf
def a(n): return rf(3*n-2, n)
  • Sage
    def a(n): return rising_factorial(3*n-2, n)

Formula

a(n) = RisingFactorial(3*n-2,n).
a(n) = n! * [x^n] 1/(1 - x)^(3*n-2).
a(n) = n! * binomial(4*n-3,n).
D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) -8*(4*n-5)*(4*n-3)*(2*n-3)*a(n-1)=0. - R. J. Mathar, May 26 2025
Showing 1-2 of 2 results.

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

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