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

0,2

Links

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

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

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);

Crossrefs

Cf. A000203, A319083.

Sequence in context: A368965 A344553 A121572 * A249924 A305307 A074543

Adjacent sequences: A340990 A340991 A340992 * A340994 A340995 A340996

Keyword

nonn

Author

Alois P. Heinz, Feb 01 2021

Status

approved