OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..3260 (terms 0..1000 from Alois P. Heinz)
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A001405(j).
a(n) ~ 2^(n - 1/6) * exp(3*(n/2)^(1/3) - 2 + S) / (sqrt(3*Pi) * n^(5/6)), where S = Sum_{k>=2} (sqrt(1/(1 - 1/2^(2*k - 2))) - 1) * (2^k + 2) / (2*k) = 0.3158684977247920135402311766405977266170498097655... - Vaclav Kotesovec, May 30 2019
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(add(binomial(d,
floor(d/2))*d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
MATHEMATICA
nmax = 40; A001405 = Table[Binomial[n, Floor[n/2]], {n, 1, nmax}]; CoefficientList[Series[Product[1/(1 - x^k)^A001405[[k]], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 30 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2017
STATUS
approved