OFFSET
0,1
FORMULA
Equals sqrt(15) * log(phi) / Pi, where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
If m >= 0 and g.f. is Sum_{k>=1} (k^m * x^(k^2) / Product_{j=1..k} (1 - x^j)), then a(n) ~ A333155^m * phi^(1/2) * exp(2*Pi*sqrt(n/15)) * n^((2*m-3)/4) / (2 * 3^(1/4) * 5^(1/2)).
If m >= 0 and g.f. is Sum_{k>=1} (k^m * x^(k*(k+1)) / Product_{j=1..k} (1 - x^j)), then a(n) ~ A333155^m * exp(2*Pi*sqrt(n/15)) * n^((2*m-3)/4) / (2 * 3^(1/4) * 5^(1/2) * phi^(1/2)).
EXAMPLE
0.5932422150033691271841376173302559541109959549627957429060245786...
MAPLE
evalf(sqrt(15) * log((sqrt(5) + 1)/2) / Pi, 120);
MATHEMATICA
RealDigits[Sqrt[15]*Log[GoldenRatio]/Pi, 10, 105][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Mar 09 2020
STATUS
approved