OFFSET
1,9
LINKS
R. H. Hardin and Vaclav Kotesovec, Table of n, a(n) for n = 1..5000 (first 1000 terms from R. H. Hardin)
FORMULA
G.f.: Product_{j>=1} (1 + x^(6j-3)/(1-x^(2j-1))). - Emeric Deutsch, Jun 26 2009
a(n) ~ (6*c + Pi^2)^(1/4) * exp(sqrt((6*c + Pi^2)*n/3)) / (4*3^(1/4)*sqrt(Pi) * n^(3/4)), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-3*x)) dx = -0.77271248407593487127235205445116662610863126869049971822566... . - Vaclav Kotesovec, Jan 05 2016
EXAMPLE
a(15)=5 because we have 333, (2^6)(1^3), (2^5)(1^5), (2^4)(1^7), and (2^3)(1^9).
MAPLE
g := product(1+x^(3*(2*j-1))/(1-x^(2*j-1)), j = 1 .. 20): gser := series(g, x = 0, 80): seq(coeff(gser, x, n), n = 1 .. 72); # Emeric Deutsch, Jun 26 2009
MATHEMATICA
nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(6*k-3) / (1-x^(2*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jan 02 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin Jun 02 2009
EXTENSIONS
Minor edits by Vaclav Kotesovec, Jan 02 2016
STATUS
approved