A255965 - Asymptotic formula
(Vaclav Kotesovec, Mar 12 2015)

a(n) ~ Zeta(9)^(1848353/32659200) / (3 * 2^(3594847/10886400) * sqrt(Pi) * n^(18177953/32659200))
 * exp(Zeta'(-1)/7 - 7*Zeta(3)/(80*Pi^2) + 7*Zeta(5)/(64*Pi^4) - 3*Zeta(7)/(128*Pi^6) - Pi^64/(1777299241697280000000000000000 * Zeta(9)^7) + (Pi^48 * Zeta(7))/(4701849845760000000000 * Zeta(9)^6) - Pi^46/(1469328076800000000000 * Zeta(9)^5) - Pi^32 * Zeta(7)^2/(38698352640000 * Zeta(9)^5) + (29 * Pi^32 * Zeta(5))/(22674816000000000 * Zeta(9)^4) + (Pi^30 * Zeta(7))/(7255941120000 * Zeta(9)^4) + (25 * Pi^16 * Zeta(7)^3)/(23887872 * Zeta(9)^4) - 43*Pi^28/(212576400000000 * Zeta(9)^3) - (29 * Pi^16 * Zeta(5) * Zeta(7))/(139968000 * Zeta(9)^3) - 25 * Pi^14 * Zeta(7)^2/(4478976 * Zeta(9)^3) - 390625 * Zeta(7)^4/(55296 * Zeta(9)^3) + Pi^16 * Zeta(3)/(816480000 * Zeta(9)^2) + 29 * Pi^14 * Zeta(5)/(52488000 * Zeta(9)^2) + 407 * Pi^12 * Zeta(7)/(41990400 * Zeta(9)^2) + (3625 * Zeta(5) * Zeta(7)^2)/(864 * Zeta(9)^2) - 7*Pi^10/(1166400 * Zeta(9)) - 841*Zeta(5)^2/(2025 * Zeta(9)) - 25 * Zeta(3) * Zeta(7)/(252 * Zeta(9)) + Zeta'(-7)/5040 + 5*Zeta'(-5)/144 + 29*Zeta'(-3)/90
 + ((16169 * Pi^56)/(4685167094776012800000000000000 * 2^(1/3) * Zeta(9)^(55/9)) - (4921 * Pi^40 * Zeta(7))/(4284560671948800000000 * 2^(1/3) * Zeta(9)^(46/9)) + (133 * Pi^38)/(35704672266240000000 * 2^(1/3) * Zeta(9)^(37/9)) + (133 * Pi^24 * Zeta(7)^2)/(1175462461440 * 2^(1/3) * Zeta(9)^(37/9)) - (551 * Pi^24 * Zeta(5))/(76527504000000 * 2^(1/3) * Zeta(9)^(28/9)) - (19 * Pi^22 * Zeta(7))/(32651735040 * 2^(1/3) * Zeta(9)^(28/9)) - (59375 * Pi^8 * Zeta(7)^3)/(20155392 * 2^(1/3) * Zeta(9)^(28/9)) + (1439 * Pi^20)/(1700611200000 * 2^(1/3) * Zeta(9)^(19/9)) + (29 * Pi^8 * Zeta(5) * Zeta(7))/(34992 * 2^(1/3) * Zeta(9)^(19/9)) + (3125 * Pi^6 * Zeta(7)^2)/(279936 * 2^(1/3) * Zeta(9)^(19/9)) - (Pi^8 * Zeta(3))/(113400 * 2^(1/3) * Zeta(9)^(10/9)) - (29 * Pi^6 * Zeta(5))/(14580 * 2^(1/3) * Zeta(9)^(10/9)) - (7 * Pi^4 * Zeta(7))/(864 * 2^(1/3) * Zeta(9)^(10/9))) * n^(1/9)
 + ((-6061 * Pi^48)/(289207845356544000000000000 * 2^(2/3) * Zeta(9)^(47/9)) + (319 * Pi^32 * Zeta(7))/(52895810764800000 * 2^(2/3) * Zeta(9)^(38/9)) - (11 * Pi^30)/(550998028800000 * 2^(2/3) * Zeta(9)^(29/9)) - (55 * Pi^16 * Zeta(7)^2)/(120932352 * 2^(2/3) * Zeta(9)^(29/9)) + (319 * Pi^16 * Zeta(5))/(7873200000 * 2^(2/3) * Zeta(9)^(20/9)) + (11 * Pi^14 * Zeta(7))/(5038848 * 2^(2/3) * Zeta(9)^(20/9)) + (171875 * Zeta(7)^3)/(31104 * 2^(2/3) * Zeta(9)^(20/9)) - (407 * Pi^12)/(131220000 * 2^(2/3) * Zeta(9)^(11/9)) - (145 * Zeta(5) * Zeta(7))/(54 * 2^(2/3) * Zeta(9)^(11/9)) + Zeta(3)/(7 * 2^(2/3) * Zeta(9)^(2/9))) * n^(2/9)
 + ((7 * Pi^40)/(110199605760000000000 * Zeta(9)^(13/3)) - (7 * Pi^24 * Zeta(7))/(453496320000 * Zeta(9)^(10/3)) + Pi^22/(18895680000 * Zeta(9)^(7/3)) + (25 * Pi^8 * Zeta(7)^2)/(31104 * Zeta(9)^(7/3)) - (29 * Pi^8 * Zeta(5))/(243000 * Zeta(9)^(4/3)) - (25 * Pi^6 * Zeta(7))/(7776 * Zeta(9)^(4/3)) + (7 * Pi^4)/(1800 * Zeta(9)^(1/3))) * n^(1/3)
 + ((-143 * Pi^32)/(367332019200000000 * 2^(1/3) * Zeta(9)^(31/9)) + (13 * Pi^16 * Zeta(7))/(167961600 * 2^(1/3) * Zeta(9)^(22/9)) - Pi^14/(3499200 * 2^(1/3) * Zeta(9)^(13/9)) - (625 * Zeta(7)^2)/(288 * 2^(1/3) * Zeta(9)^(13/9)) + (29 * Zeta(5))/(30 * 2^(1/3) * Zeta(9)^(4/9))) * n^(4/9)
 + ((7 * Pi^24)/(2834352000000 * 2^(2/3) * Zeta(9)^(23/9)) - (Pi^8 * Zeta(7))/(2592 * 2^(2/3) * Zeta(9)^(14/9)) + Pi^6/(540 * 2^(2/3) * Zeta(9)^(5/9))) * n^(5/9)
 + (-Pi^16/(116640000 * Zeta(9)^(5/3)) + (25 * Zeta(7))/(24 * Zeta(9)^(2/3))) * n^(2/3)
 + (Pi^8/(12600 * 2^(1/3) * Zeta(9)^(7/9))) * n^(7/9)
 + ((9 * Zeta(9)^(1/9))/(4 * 2^(2/3))) * n^(8/9))