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.

A355096 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(log(1+x)).

Original entry on oeis.org

1, 2, 6, 16, -12, -492, 628, 63488, -408112, -20183928, 444216616, 9449212584, -679737200176, 2572902869080, 1276955484043864, -53294396490490656, -1891642613896659904, 314259171327032640928, -8590801196259162852288, -1381246455381881103425424
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

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

Formula

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

A355105 E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(log(1+x)).

Original entry on oeis.org

1, 3, 18, 135, 1044, 6210, -5994, -760347, -3009960, 261689616, 1960394400, -220644396522, -1043258760828, 366570209524896, -3109452797977470, -972076070389224105, 36160406771040130320, 3274635904971823559880, -331428842765036684941320
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*i*sum(j=0, i-1, stirling(i-1, j, 1)*v[j+1])); v;

Formula

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).
a(n) = 3 * n * A355097(n-1) for n>0.

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.