A370733 a(n) = 5^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/5).

1, 10, 550, 19750, 921250, 32011250, 1563143750, 58080093750, 2719958906250, 113913469531250, 5214823539843750, 228024893230468750, 10704801509316406250, 482674223446582031250, 22664252188144042968750, 1053427002068999511718750, 49776941230938518066406250

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• nonn

Crossrefs

Cf. A070933 (m=1), A370713 (m=2), A370715 (m=3), A370732 (m=4).

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1/(1-2*(25*x)^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - 2*(25*x)^k)^(1/5).

a(n) ~ 50^n / (Gamma(1/5) * QPochhammer(1/2)^(1/5) * n^(4/5)).