OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1/(1 - x)) * Product_{k>=2} 1/(1 - x^k)^(phi(k^2)/2), where phi() is the Euler totient function. - Ilya Gutkovskiy, May 28 2019
a(n) ~ exp(4*sqrt(Pi)*n^(3/4)/(3*5^(1/4)) + 3*zeta(3)/(2*Pi^2)) / (2^(3/2)*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 28 2024
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 10*x^4 + 23*x^5 + 40*x^6 + 86*x^7 + ...
where
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 19*x^4/4 + 51*x^5/5 + 48*x^6/6 + 148*x^7/7 + 147*x^8/8 + 253*x^9/9 + 253*x^10/10 + ... + A056789(n)*x^n/n + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[1/Sqrt[1-x] * Product[1/(1 - x^k)^(k*EulerPhi[k]/2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 28 2024 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 07 2013
STATUS
approved