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.

A368286 Expansion of e.g.f. exp(-x) / (1 + 2*log(1 - x)).

Original entry on oeis.org

1, 1, 7, 51, 521, 6617, 100903, 1795091, 36497601, 834825089, 21217022903, 593152248323, 18089914384425, 597680325734905, 21266014041519799, 810711731123810051, 32966705053762073665, 1424339658492670445121, 65159114638457033834791
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 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, (j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368283 Expansion of e.g.f. exp(2*x) / (1 + log(1 - x)).

Original entry on oeis.org

1, 3, 11, 52, 320, 2486, 23402, 258252, 3263528, 46433648, 734322672, 12776283136, 242519067056, 4987324250416, 110454579648688, 2621008072506592, 66341399843669760, 1784150447268259456, 50804574646886197888, 1527058892582680257024
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=2^i+sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(n) = 2^n + Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ n! * exp(n + 2 - 2*exp(-1)) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 29 2023

A368287 Expansion of e.g.f. exp(-2*x) / (1 + 2*log(1 - x)).

Original entry on oeis.org

1, 0, 6, 32, 356, 4456, 68096, 1211136, 24625408, 563266240, 14315378880, 400206928128, 12205482237824, 403262088466688, 14348434923733504, 546996936260529152, 22243031618999642112, 961019064912965103616, 43963636798214215278592
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-2)^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

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