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

%I A340993 #11 Jul 25 2024 08:34:24
%S A340993 1,3,17,120,885,6713,51932,407214,3224845,25733325,206584437,
%T A340993 1666561042,13498994796,109713432390,894291885000,7307812510970,
%U A340993 59847327807597,491062976039618,4036174402666925,33224883837921930,273873806179142545,2260338391869532332
%N A340993 a(n) is the (2n)-th term of the n-fold self-convolution of the sum of divisors function sigma.
%H A340993 Alois P. Heinz, <a href="/A340993/b340993.txt">Table of n, a(n) for n = 0..1080</a>
%F A340993 a(n) = [x^(2n)] (Sum_{j>=1} sigma(j)*x^j)^n.
%F A340993 a(n) = A319083(2n,n).
%F A340993 a(n) ~ c * d^n / sqrt(n), where d = 8.455610430383829836198938524980234226695900064615457328971640722426861925... and c = 0.352126317954512592610958969393229871240824031029408304023118123356... - _Vaclav Kotesovec_, Jul 25 2024
%p A340993 b:= proc(n, k) option remember; `if`(k=0, 1,
%p A340993       `if`(k=1, numtheory[sigma](n+1), (q->
%p A340993        add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A340993     end:
%p A340993 a:= n-> b(n$2):
%p A340993 seq(a(n), n=0..23);
%Y A340993 Cf. A000203, A319083.
%K A340993 nonn
%O A340993 0,2
%A A340993 _Alois P. Heinz_, Feb 01 2021