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.

A368453 Expansion of e.g.f. 3*exp(x) / (4 - exp(3*x)).

Original entry on oeis.org

1, 2, 8, 52, 452, 4892, 63508, 962012, 16654772, 324375292, 7019618708, 167098274972, 4339293330292, 122075401356092, 3698469101172308, 120054668185331932, 4156854586083305012, 152925374174876071292, 5956866331612558316308, 244927333201908131524892
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 3^(j-1)*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368441 Expansion of e.g.f. exp(x) / (4 - 3*exp(3*x)).

Original entry on oeis.org

1, 10, 208, 6508, 271468, 14154580, 885638908, 64649204308, 5393387534428, 506188870889140, 52786278954586108, 6055112126576175508, 757725480419984012188, 102722055234542078115700, 14996854976334688765608508, 2345848207305916218955201108
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+3*sum(j=1, i, 3^j*binomial(i, j)*v[i-j+1])); v;

Formula

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