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.

Previous Showing 11-13 of 13 results.

A234529 3*binomial(10*n+6,n)/(5*n+3).

Original entry on oeis.org

1, 6, 75, 1190, 21285, 409266, 8259888, 172593900, 3701885490, 81033954430, 1803028662435, 40658396849388, 927146157991625, 21342995124948000, 495322997953271580, 11576581508367256920, 272239271289546497046, 6437043284012559773100
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=10, r=6.

Links

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234527, A234528, A234570, A234571, A234573, A229963.

Programs

  • Magma
    [3*Binomial(10*n+6, n)/(5*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013
  • Mathematica
    Table[3 Binomial[10 n + 6, n]/(5 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 27 2013 *)
  • PARI
    a(n) = 3*binomial(10*n+6,n)/(5*n+3);
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/3))^6+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=6.

A234570 7*binomial(10*n+7,n)/(10*n+7).

Original entry on oeis.org

1, 7, 91, 1470, 26565, 514206, 10426416, 218618940, 4701550770, 103134123820, 2298706645235, 51909777109596, 1185134654128425, 27309853977084000, 634361032466470620, 14837590383963667320, 349163392095422769942, 8260872214482785042145, 196380752260155290992675
Offset: 0

Views

Author

Tim Fulford, Dec 28 2013

Keywords

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=7.

Links

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234527, A234528, A234529, A234571, A234573, A229963.

Programs

  • Magma
    [7*Binomial(10*n+7, n)/(10*n+7): n in [0..30]];
  • Mathematica
    Table[7 Binomial[10 n + 7, n]/(10 n + 7), {n, 0, 30}]
  • PARI
    a(n) = 7*binomial(10*n+7,n)/(10*n+7);
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/7))^7+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=7.

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 11-13 of 13 results.

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