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

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

Offset: 0

Author

Alois P. Heinz, Feb 01 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1080

Crossrefs

Cf. A000203, A319083.

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