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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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.

Links

Crossrefs

Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234510, A234513, A232265.

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.

A235339 a(n) = 9*binomial(11*n+9,n)/(11*n+9).

Original entry on oeis.org

1, 9, 135, 2460, 49725, 1072197, 24163146, 562311720, 13409091540, 325949656825, 8046743477058, 201198155083200, 5084704634041305, 129673310477725350, 3332952595603387800, 86250038091202771344, 2245329811618166111985
Offset: 0

Views

Author

Tim Fulford, Jan 06 2014

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p = 11, r = 9.

Links

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235340, A069271, A118970, A212073, A230388, A233834, A234465, A234510, A234571.

Programs

  • Magma
    [9*Binomial(11*n+9, n)/(11*n+9): n in [0..30]];
  • Mathematica
    Table[9 Binomial[11 n + 9, n]/(11 n + 9), {n, 0, 30}]
  • PARI
    a(n) = 9*binomial(11*n+9,n)/(11*n+9);
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/9))^9+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p = 11, r = 9.
O.g.f. A(x) = 1/x * series reversion (x/C(x)^9), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/9) is the o.g.f. for A230388. - Peter Bala, Oct 14 2015
Previous Showing 11-12 of 12 results.

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