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 1-3 of 3 results.

A368454 Expansion of e.g.f. 2*exp(-x) / (3 - exp(2*x)).

Original entry on oeis.org

1, 0, 3, 12, 93, 840, 9183, 117012, 1704153, 27921360, 508302363, 10178888412, 222365364213, 5262547606680, 134124963385143, 3662574088282212, 106682195378484273, 3301614846549616800, 108189336403552025523, 3742170760095124874412
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)^i+sum(j=1, i, 2^(j-1)*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368443 Expansion of e.g.f. exp(-x) / (4 - 3*exp(2*x)).

Original entry on oeis.org

1, 5, 73, 1517, 42193, 1466645, 61177753, 2977205117, 165583073953, 10360379100965, 720265883283433, 55081115403503117, 4595165623000889713, 415299796681103596085, 40420990463421954662713, 4215173033091627126703517, 468870152072269125977393473
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)^i+3*sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368438 Expansion of e.g.f. exp(x) / (3 - 2*exp(2*x)).

Original entry on oeis.org

1, 5, 49, 725, 14305, 352805, 10441489, 360526325, 14226677185, 631571457605, 31152937452529, 1690317145051925, 100052040656540065, 6415726051515362405, 443047566486308303569, 32780692416679034537525, 2587108326603274903810945
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+2*sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;

Formula

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