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.

A367235 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^4.

Original entry on oeis.org

1, 1, 7, 50, 399, 3422, 30798, 286974, 2744947, 26798010, 265945022, 2674970684, 27209385886, 279412999031, 2892787737002, 30161921520976, 316440334960563, 3338105334701396, 35385133077851602, 376732207920371784, 4026682585718602014
Offset: 0

Views

Author

Seiichi Manyama, Nov 11 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=4, t=3, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));

Formula

If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).

A378567 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+3*k-1,n-k).

Original entry on oeis.org

1, 1, 11, 88, 715, 5951, 50288, 429696, 3702987, 32125390, 280211701, 2454992618, 21588647392, 190444368401, 1684556756320, 14935618142768, 132695019071499, 1181070210132582, 10529299131757754, 94005323670592130, 840373149466892965, 7521508912742542806
Offset: 0

Views

Author

Seiichi Manyama, Dec 01 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_]:=SeriesCoefficient[ 1/(1 - x/(1 - x)^4)^n,{x,0,n}]; Array[a,22,0] (* Stefano Spezia, Dec 01 2024 *)
  • PARI
    a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+3*k-1, n-k));

Formula

a(n) = [x^n] 1/(1 - x/(1 - x)^4)^n.
Showing 1-2 of 2 results.