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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.
2
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
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
Sequence in context: A368965 A344553 A121572 * A249924 A305307 A074543
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 01 2021
STATUS
approved