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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1080
Programs
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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