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.

A340993 a(n) is the (2n)-th term of the n-fold self-convolution of the sum of divisors function sigma.

Original entry on oeis.org

1, 3, 17, 120, 885, 6713, 51932, 407214, 3224845, 25733325, 206584437, 1666561042, 13498994796, 109713432390, 894291885000, 7307812510970, 59847327807597, 491062976039618, 4036174402666925, 33224883837921930, 273873806179142545, 2260338391869532332
Offset: 0

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Author

Alois P. Heinz, Feb 01 2021

Keywords

Crossrefs

Programs

  • Maple
    b:= proc(n, k) option remember; `if`(k=0, 1,
          `if`(k=1, numtheory[sigma](n+1), (q->
           add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
        end:
    a:= n-> b(n$2):
    seq(a(n), n=0..23);

Formula

a(n) = [x^(2n)] (Sum_{j>=1} sigma(j)*x^j)^n.
a(n) = A319083(2n,n).
a(n) ~ c * d^n / sqrt(n), where d = 8.455610430383829836198938524980234226695900064615457328971640722426861925... and c = 0.352126317954512592610958969393229871240824031029408304023118123356... - Vaclav Kotesovec, Jul 25 2024