OFFSET
0,2
FORMULA
a(n) = Sum_{d|n} 2^(d-n/d+1) * binomial(d,n/d-1) for n > 0.
If p is an odd prime, a(p) = 2^p.
MATHEMATICA
a[n_] := DivisorSum[n, 2^(# - n/# + 1) * Binomial[#, n/# - 1] &]; a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Aug 02 2023 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x*(2+x^k))^k))
(PARI) a(n) = if(n==0, 1, sumdiv(n, d, 2^(d-n/d+1)*binomial(d, n/d-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 20 2023
STATUS
approved