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.

A363661 a(n) = Sum_{d|n} (n/d)^d * binomial(d+n,n).

Original entry on oeis.org

2, 12, 32, 150, 282, 1890, 3488, 21582, 54650, 282612, 705564, 4072224, 10400782, 55006530, 158987232, 790611350, 2333606526, 11573213196, 35345264180, 168673694070, 540848064614, 2500462200182, 8233430728152, 37445946291600, 126411051769652
Offset: 1

Views

Author

Seiichi Manyama, Jun 14 2023

Keywords

Comments

All terms are even. - Robert Israel, Nov 23 2023

Crossrefs

Programs

  • Maple
    f:= proc(n) local d;
       add((n/d)^d * binomial(n+d,n), d = numtheory:-divisors(n))
    end proc:
    map(f, [$1..30]); # Robert Israel, Nov 23 2023
  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n, n] &]; Array[a, 30] (* Amiram Eldar, Jul 05 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n, n));

Formula

a(n) = [x^n] Sum_{k>0} (1/(1 - k*x^k)^(n+1) - 1).

A363662 a(n) = Sum_{d|n} (n/d)^n * binomial(d+n,n).

Original entry on oeis.org

2, 18, 128, 1590, 19002, 353304, 6591776, 154083654, 3878583770, 110647791078, 3423740752764, 116116072618104, 4240251502692142, 166761491097360240, 7006327371058071648, 313637735782416564806, 14890324713956395361406, 747610406539465959084870
Offset: 1

Views

Author

Seiichi Manyama, Jun 14 2023

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n, n] &]; Array[a, 20] (* Amiram Eldar, Jul 12 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^n*binomial(d+n, n));

Formula

a(n) = [x^n] Sum_{k>0} (1/(1 - (k*x)^k)^(n+1) - 1).
Showing 1-2 of 2 results.