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.

A355120 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2 * log(1+x)).

Original entry on oeis.org

1, 1, 3, 26, 654, 45084, 7934924, 3381663872, 3365978050576, 7632454575648720, 38732162420625498608, 434139952882119137261024, 10640704036253473615712677216, 565765176687479152385624223741568, 64834956096893473256448986077914291328
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * Stirling1(n,k) * a(k-1).

A355208 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * log(1+x)).

Original entry on oeis.org

1, 2, 6, 28, 236, 4400, 197552, 20430656, 4600591488, 2179887358272, 2130534442932416, 4243581375963409024, 17097951082212352465536, 138722374358947243721661440, 2260145794657531151029628653568, 73822509077371344216463442074629120
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2022

Keywords

Crossrefs

Programs

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

Formula

a(1) = 1; a(n+1) = Sum_{k=1..n} 2^k * Stirling1(n,k) * a(k).

A355124 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * log(1+x)).

Original entry on oeis.org

1, 1, 4, 42, 1168, 84180, 15107328, 6495857312, 6492989426432, 14753072834027424, 74941835564789489280, 840421638561217307501632, 20603672787268830442103493120, 1095629510349075557617215030858112, 125563465926494619940863277689861766144
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} 2^k * Stirling1(n-1,k) * a(k).
a(n) = n * A355133(n-1) for n>0.
Showing 1-3 of 3 results.