OFFSET
1,3
COMMENTS
Inverse Euler transform of A000129.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
-1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A000129.
a(n) ~ (1 + sqrt(2))^n/n. - Vaclav Kotesovec, May 28 2019
"CHK" (necklace, identity, unlabeled) transform of A000045. - Alois P. Heinz, May 19 2022
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(j-1-a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> combinat[fibonacci](n)+b(n, n-1):
seq(a(n), n=1..34); # Alois P. Heinz, May 19 2022
MATHEMATICA
nmax = 34; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + x^k/(1 - 2 x^k - x^(2 k))]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 40; s = ConstantArray[0, nmax]; Do[s[[j]] = j*Fibonacci[j, 2] - Sum[s[[d]]*Fibonacci[j - d, 2], {d, 1, j - 1}], {j, 1, nmax}]; Table[Sum[MoebiusMu[k/d]*s[[d]], {d, Divisors[k]}]/k, {k, 1, nmax}] (* Vaclav Kotesovec, Aug 10 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 27 2019
STATUS
approved