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 1-2 of 2 results.

A351526 Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1+ x)))))^2 / 2.

Original entry on oeis.org

1, -12, 152, -2210, 36976, -704837, 15132932, -362099010, 9566898126, -276863733707, 8715530417502, -296641340905299, 10858928017129838, -425542158316462627, 17779220784851800828, -789053832262002586555, 37076561046965367191298
Offset: 2

Views

Author

Seiichi Manyama, Feb 13 2022

Keywords

Crossrefs

Column 2 of A039816.
Cf. A000310, A341587, A351514, A351525, A351527.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(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, 4)*T(n-k, 4));

Formula

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000310(k) * A000310(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

Column 2 of A039817.
Cf. A000359, A341587, A351515, A351525, A351526.

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 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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