OFFSET
0,3
COMMENTS
Denominators of c(n) are 2^A004134(n).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Geoffrey B. Campbell and A. Zujev, Some almost partition theoretic identities, Preprint, 2016.
N. J. A. Sloane, Transforms
FORMULA
Numerators of c(n), where c(n) = (1/(4*n))*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(add(
d/4, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
end:
a:= n-> numer(b(n)):
seq(a(n), n=0..30); # Alois P. Heinz, Jul 28 2017
MATHEMATICA
c[n_] := c[n] = If[n == 0, 1,
(1/(4n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]];
a[n_] := Numerator[c[n]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 24 2022 *)
CROSSREFS
KEYWORD
easy,nonn,frac
AUTHOR
Vladeta Jovovic, Apr 17 2001
STATUS
approved