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.

A351513 Expansion of e.g.f. (exp(exp(exp(x)-1)-1)-1)^2 / 2.

Original entry on oeis.org

1, 9, 75, 660, 6288, 65051, 728556, 8792910, 113805204, 1572387410, 23094192960, 359209182397, 5896792771795, 101854538628396, 1846058978130172, 35021271971160507, 693843099578350329, 14326635965967487711, 307729547549467823822, 6864250658908517748384
Offset: 2

Views

Author

Seiichi Manyama, Feb 12 2022

Keywords

Crossrefs

Column 2 of A039811.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(x)-1)-1)-1)^2/2))
    
  • PARI
    T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
    a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 3)*T(n-k, 3));

Formula

a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000258(k) * A000258(n-k).

A351514 Expansion of e.g.f. (exp(exp(exp(exp(x)-1)-1)-1)-1)^2 / 2.

Original entry on oeis.org

1, 12, 136, 1650, 21904, 318521, 5051988, 86910426, 1612648066, 32107793135, 682724688430, 15439016490989, 369914992674530, 9359103270641290, 249292192469843244, 6971850327184526783, 204215496402215939638, 6251233458455082035922
Offset: 2

Views

Author

Seiichi Manyama, Feb 12 2022

Keywords

Crossrefs

Column 2 of A039812.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(x)-1)-1)-1)-1)^2/2))
    
  • PARI
    T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
    a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 4)*T(n-k, 4));

Formula

a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000307(k) * A000307(n-k).

A351527 Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1 + log(1+ x))))))^2 / 2.

Original entry on oeis.org

1, -15, 235, -4200, 86020, -2001055, 52305780, -1520815230, 48747603100, -1709228504170, 65115320810260, -2679459929923699, 118482699493123571, -5604477255138004835, 282449438671531808676, -15111729578894643263239
Offset: 2

Views

Author

Seiichi Manyama, Feb 13 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+log(1+log(1+x)))))^2/2))
    
  • PARI
    T(n, k) = if(k==0, n==1, sum(j=0, n, abs(stirling(n, j, 1))*T(j, k-1)));
    a(n) = (-1)^n*sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));

Formula

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000359(k) * A000359(n-k).
Showing 1-3 of 3 results.