A000428 - Asymptotic formula
(Vaclav Kotesovec, Mar 12 2015)

a(n) ~ Pi^(275/24192) / (4 * 2^(12371/193536) * 3^(12371/64512) * 5^(12371/96768) * n^(109139/193536))
 * exp(Zeta'(-1)/6 - (1051 * Zeta(3))/(1120 * Pi^2) + (250833 * Zeta(5))/(1568 * Pi^4) - (4600625761 * Zeta(7))/(1185408 * Pi^6) + (1537734375 * Zeta(5)^2 * Zeta(7))/(16 * Pi^16) + (34171875 * Zeta(3) * Zeta(7)^2)/(4 * Pi^16) - (217845703125 * Zeta(5) * Zeta(7)^2)/(28 * Pi^18) + (58282012265625 * Zeta(7)^3)/(392 * Pi^20) + (157641800537109375 * Zeta(5) * Zeta(7)^4)/(4 * Pi^32) - (8933035363769531250 * Zeta(7)^5)/(7 * Pi^34) + (21547663610916137695312500 * Zeta(7)^7)/(7 * Pi^48) + Zeta'(-5)/48 + (5 * Zeta'(-3))/16
 + ((1701173 * 5^(1/4) * Pi)/(3556224 * 2^(7/8) * 3^(5/8)) - (151875 * 3^(3/8) * 5^(1/4) * Zeta(5)^2)/(16 * 2^(7/8) * Pi^9) - (3375 * 3^(3/8) * 5^(1/4) * Zeta(3) * Zeta(7))/(2 * 2^(7/8) * Pi^9) + (193640625 * 3^(3/8) * 5^(1/4) * Zeta(5) * Zeta(7))/(224 * 2^(7/8) * Pi^11) - (429647844375 * 3^(3/8) * 5^(1/4) * Zeta(7)^2)/(25088 * 2^(7/8) * Pi^13) - (794047587890625 * 3^(3/8) * 5^(1/4) * Zeta(5) * Zeta(7)^3)/(128 * 2^(7/8) * Pi^25) + (2812251873779296875 * 3^(3/8) * 5^(1/4) * Zeta(7)^4)/(14336 * 2^(7/8) * Pi^27) - (4477125661379241943359375 * 3^(3/8) * 5^(1/4) * Zeta(7)^6)/(8192 * 2^(7/8) * Pi^41)) * n^(1/8)
 + ((sqrt(5) * Zeta(3))/(2^(3/4) * 3^(1/4) * Pi^2) - (2125 * (3/2)^(3/4) * sqrt(5) * Zeta(5))/(56 * Pi^4) + (3911455 * sqrt(5) * Zeta(7))/(1568 * 2^(3/4) * 3^(1/4) * Pi^6) + (7688671875 * (3/2)^(3/4) * sqrt(5) * Zeta(5) * Zeta(7)^2)/(16 * Pi^18) - (3267685546875 * (3/2)^(3/4) * sqrt(5) * Zeta(7)^3)/(224 * Pi^20) + (6148030220947265625 * (3/2)^(3/4) * sqrt(5) * Zeta(7)^5)/(128 * Pi^34)) * n^(1/4)
 + ((-100069 * Pi)/(105840 * 2^(5/8) * 3^(7/8) * 5^(1/4)) - (455625 * 3^(1/8) * 5^(3/4) * Zeta(5) * Zeta(7))/(4 * 2^(5/8) * Pi^11) + (710015625 * 3^(1/8) * 5^(3/4) * Zeta(7)^2)/(224 * 2^(5/8) * Pi^13) - (3254038154296875 * 3^(1/8) * 5^(3/4) * Zeta(7)^4)/(256 * 2^(5/8) * Pi^27)) * n^(3/8)
 + ((225 * sqrt(3/2) * Zeta(5))/(4 * Pi^4) - (31875 * sqrt(3/2) * Zeta(7))/(28 * Pi^6) + (23066015625 * sqrt(3/2) * Zeta(7)^3)/(4 * Pi^20)) * sqrt(n)
 + ((17 * 5^(1/4) * Pi)/(63 * 2^(3/8) * 3^(1/8)) - (2278125 * 3^(7/8) * 5^(1/4) * Zeta(7)^2)/(4 * 2^(3/8) * Pi^13)) * n^(5/8)
 + ((225 * (3/2)^(1/4) * sqrt(5) * Zeta(7))/Pi^6) * n^(3/4)
 + ((4 * 2^(7/8) * Pi)/(7 * 3^(3/8) * 5^(1/4))) * n^(7/8))