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.

A368285 Expansion of e.g.f. exp(2*x) / (1 + 2*log(1 - x)).

Original entry on oeis.org

1, 4, 22, 168, 1700, 21560, 328576, 5844608, 118827264, 2717955776, 69076424384, 1931128212992, 58895387322240, 1945869352171264, 69235812945551872, 2639436090012161024, 107329778640349652992, 4637225944423696109568, 212138681191492565180416
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).
a(n) ~ n! * exp(n/2 + 2 - 2*exp(-1/2)) / (2 * (exp(1/2) - 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).

A368446 Expansion of e.g.f. exp(-x) / (1 + log(1 - 2*x)).

Original entry on oeis.org

1, 1, 9, 81, 1025, 16177, 306793, 6791201, 171849153, 4892782241, 154792866953, 5387090968113, 204528939571521, 8412441383512657, 372629008281155177, 17684630326318986881, 895251144144309285505, 48152984520621412552257
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*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

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