OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
FORMULA
G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^(k*A074206(k)).
a(n) ~ ((1 - 2^(2+r)) * Gamma(2+r) * zeta(2+r))^(1/(50*(2+r))) * exp(12/625 + 2^(1/(2+r) - 1) * (2+r) * ((1 - 2^(2+r)) * Gamma(2+r) * zeta(2+r))^(1/(2+r)) / (zeta'(r)^(1/(2+r)) * (1+r)) * n^((1+r)/(2+r))) / (A^(144/625) * 2^((3 + 2*r)/(50*(2 + r))) * zeta'(r)^(1/(50*(2+r))) * sqrt(Pi*(2+r)) * n^(1/2 + 1/(50*(2+r)))), where r = A107311 is the root of the equation zeta(r)=2 and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Mar 18 2021
EXAMPLE
G.f.: A(x) = 1 + 2*x + 6*x^2 + 16*x^3 + 46*x^4 + 104*x^5 + 268*x^6 + 596*x^7 + 1406*x^8 + 3060*x^9 + ...
MATHEMATICA
terms = 32; A[_] = 1; Do[A[x_] = (1 + x)/(1 - x) Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 18 2019
STATUS
approved