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.

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A023839 Sum of exponents in prime-power factorization of C(5n,n-2).

Original entry on oeis.org

0, 2, 3, 5, 6, 7, 8, 9, 9, 10, 10, 13, 12, 15, 13, 15, 15, 14, 16, 18, 16, 18, 19, 19, 22, 23, 23, 24, 23, 23, 22, 26, 22, 24, 25, 24, 24, 28, 26, 27, 28, 27, 28, 33, 30, 29, 31, 33, 33, 34, 35, 38, 37, 39, 37, 37, 38, 38, 42, 40, 38, 40, 39, 41, 38, 36, 38, 43, 40, 44, 42, 44, 42, 44, 45, 48, 49, 49
Offset: 2

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Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004344, A023837, A023838, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, n - 2]], {n, 2, 79}] (* Ivan Neretin, Nov 08 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-2)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004344(n-2)).
a(n) = A023838(n) - A001222(4*n+2) + A001222(n-1). (End)

Extensions

Offset corrected to 2 by Ivan Neretin, Nov 08 2017

A233738 2*binomial(5*n+10, n)/(n+2).

Original entry on oeis.org

1, 10, 95, 920, 9135, 92752, 959595, 10084360, 107375730, 1156073100, 12565671261, 137702922560, 1519842008360, 16880051620320, 188519028884675, 2115822959020080, 23851913523156675, 269958280013904870, 3066451080298820830, 34946186787944832400
Offset: 0

Views

Author

Tim Fulford, Dec 15 2013

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=10.

Links

Crossrefs

Cf. A000108, A002294, A004344, A118969, A118971, A143546, A233668, A233669, A233736, A233737.

Programs

  • Magma
    [2*Binomial(5*n+10, n)/(n+2): n in [0..30]]; // Vincenzo Librandi, Dec 16 2013
  • Maple
    A233738:=n->2*binomial(5*n+10,n)/(n+2): seq(A233738(n), n=0..30); # Wesley Ivan Hurt, Sep 07 2014
  • Mathematica
    Table[2 Binomial[5 n + 10, n]/(n + 2), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *)
  • PARI
    a(n) = 2*binomial(5*n+10,n)/(n+2);
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(1/2))^10+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=5, r=10.
a(n) = 2*A004344(n)/(n+2). - Wesley Ivan Hurt, Sep 07 2014
G.f.: hypergeom([2, 11/5, 12/5, 13/5, 14/5], [11/4, 3, 13/4, 7/2], (3125/256)*x). - Robert Israel, Sep 07 2014
D-finite with recurrence 8*(2*n+5)*(4*n+7)*(n+2)*(4*n+9)*a(n) -(n+1)*(13877*n^3+45630*n^2+46579*n+14034)*a(n-1) +210*(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)*a(n-2)=0. - R. J. Mathar, Nov 22 2024
D-finite with recurrence 8*n*(2*n+5)*(4*n+7)*(n+2)*(4*n+9)*a(n) -5*(5*n+6)*(5*n+7)*(5*n+8)*(5*n+9)*(n+1)*a(n-1)=0. - R. J. Mathar, Nov 22 2024
Showing 1-2 of 2 results.

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

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