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.

A364161 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).

Original entry on oeis.org

1, 1, 2, 5, 15, 47, 153, 514, 1769, 6205, 22102, 79733, 290721, 1069688, 3966739, 14810348, 55627778, 210046102, 796864028, 3035912900, 11610468138, 44556451207, 171529074168, 662238211929, 2563524741603, 9947573055828, 38687704042595
Offset: 0

Views

Author

Seiichi Manyama, Aug 28 2023

Keywords

Crossrefs

Programs

  • Maple
    A364161 := proc(n)
        add( binomial(n-2*k-1,k)*binomial(2*n-5*k+1,n-3*k)/(2*n5*k+1),k=0..floor(n/3)) ;
    end proc:
    seq(A364161(n),n=0..80); # R. J. Mathar, Aug 29 2023
  • PARI
    a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +(-2*n+7)*a(n-5) +(n-8)*a(n-6) +(n-8)*a(n-8)=0. - R. J. Mathar, Aug 29 2023

A365247 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)^4).

Original entry on oeis.org

1, 1, 2, 5, 15, 50, 177, 650, 2449, 9412, 36761, 145518, 582556, 2354557, 9594898, 39378259, 162619316, 675258452, 2817643240, 11808576745, 49683880754, 209786559004, 888676860191, 3775654643360, 16084818268474, 68694452578325, 294053067958011
Offset: 0

Views

Author

Seiichi Manyama, Aug 28 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-2*k+1, n-3*k)/(2*n-2*k+1));

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-2*k+1,n-3*k)/(2*n-2*k+1).
Showing 1-2 of 2 results.