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.

A368442 Expansion of e.g.f. exp(-x) / (3 - 2*exp(2*x)).

Original entry on oeis.org

1, 3, 33, 483, 9537, 235203, 6960993, 240350883, 9484451457, 421047638403, 20768624968353, 1126878096701283, 66701360437693377, 4277150701010241603, 295365044324205535713, 21853794944452689691683, 1724738884402183269207297, 144626802398076537956524803
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+2*sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368455 Expansion of e.g.f. 3*exp(-x) / (4 - exp(3*x)).

Original entry on oeis.org

1, 0, 4, 20, 180, 1940, 25204, 381780, 6609460, 128728340, 2785737204, 66312995540, 1722049711540, 48445655125140, 1467738434962804, 47643726641609300, 1649648835729498420, 60688474959603256340, 2363983970307953910004, 97199476595104080495060
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, 3^(j-1)*binomial(i, j)*v[i-j+1])); v;

Formula

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