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.

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

A235340 a(n) = 10*binomial(11*n+10,n)/(11*n+10).

Original entry on oeis.org

1, 10, 155, 2870, 58565, 1270752, 28765650, 671650110, 16057800980, 391139588190, 9672348219898, 242182964452000, 6127720969229265, 156431295179478200, 4024231652469275640, 104218796026870015374, 2714941275486017847825
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=10.

Links

Crossrefs

Cf. A130564, A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235339.

Programs

  • Magma
    [10*Binomial(11*n+10, n)/(11*n+10): n in [0..30]];
  • Mathematica
    Table[10 Binomial[11 n + 10, n]/(11 n + 10), {n, 0, 30}]
  • PARI
    a(n) = 10*binomial(11*n+10,n)/(11*n+10);
  • PARI
    {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/10))^10+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p=11, r=10.
From Wolfdieter Lang, Feb 15 2024: (Start)
a(n) = binomial(11*n + 9, n + 1)/(10*n + 9) which is instance k = 10 of c(k, n+1) given in a comment in A130564.
x*B(x), with the g.f. above named B(x), is the compositional inverse of y*(1 - y)^10, hence B(x)*(1 - x*B(x))^10 = 1.
G.f.: 11F10([10..20]/11, [11..20]/10; (11^11/10^10)*x) = (10/(11*x))*(1 - 10F9([-1,1,2,3,4,5,6,7,8,9]/11, [1,2,3,4,5,6,7,8,9]/10; (11^11/10^10)*x)).
(End)
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.