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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A234506 a(n) = binomial(9*n+3, n)/(3*n+1).

Original entry on oeis.org

1, 3, 30, 406, 6327, 107019, 1909908, 35399520, 674842149, 13147742322, 260626484118, 5239783981320, 106585537781775, 2189670831627678, 45366284782209600, 946815917066740800, 19887218367823853937, 420076689292591271325, 8917736795123409615060, 190161017612160607167948, 4071301730663135449185705
Offset: 0

Views

Author

Tim Fulford, Dec 27 2013

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r, n)/(n*p + r), where p=9, r=3.

Crossrefs

Programs

  • Magma
    [Binomial(9*n+3, n)/(3*n+1): n in [0..30]];
    
  • Mathematica
    Table[Binomial[9n+3, n]/(3n+1), {n, 0, 30}]
  • PARI
    a(n) = binomial(9*n+3,n)/(3*n+1);
    
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^3)^3+x*O(x^n)); polcoeff(B, n)}
    
  • Sage
    [binomial(9*n+3, n)/(3*n+1) for n in (0..30)] # G. C. Greubel, Feb 09 2021

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=3.

A234508 5*binomial(9*n+5,n)/(9*n+5).

Original entry on oeis.org

1, 5, 55, 775, 12350, 211876, 3818430, 71282640, 1366368375, 26735839650, 531838637759, 10723307329700, 218658647805780, 4501362056183300, 93426735902060000, 1952884185072496992, 41074876852203972645, 868669222741822476975, 18460669540059117038250, 394033629095915025876750, 8443512680148379948569910
Offset: 0

Views

Author

Tim Fulford, Dec 27 2013

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=5.

Crossrefs

Programs

  • Magma
    [5*Binomial(9*n+5, n)/(9*n+5): n in [0..30]];
  • Mathematica
    Table[5 Binomial[9 n + 5, n]/(9 n + 5), {n, 0, 30}]
  • PARI
    a(n) = 5*binomial(9*n+5,n)/(9*n+5);
    
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/5))^5+x*O(x^n)); polcoeff(B, n)}
    

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=5.

A234509 2*binomial(9*n+6,n)/(3*n+2).

Original entry on oeis.org

1, 6, 69, 992, 15990, 276360, 5006386, 93817152, 1803606255, 35373572460, 704995403541, 14236901646240, 290687378847684, 5990903682047592, 124463414269524000, 2603845580096662656, 54807372993836345589, 1159856934027109448130, 24663454505518980363102, 526708243449729452311200, 11291926596343014148087470
Offset: 0

Views

Author

Tim Fulford, Dec 27 2013

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=6.

Crossrefs

Programs

  • Magma
    [2*Binomial(9*n+6, n)/(3*n+2): n in [0..30]];
  • Mathematica
    Table[6 Binomial[9 n + 6, n]/(9 n + 6), {n, 0, 30}]
  • PARI
    a(n) = 2*binomial(9*n+6,n)/(3*n+2);
    
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/2))^6+x*O(x^n)); polcoeff(B, n)}
    

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=6.
Previous Showing 11-13 of 13 results.