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%I #7 Feb 29 2024 06:23:56
%S 1,10,550,19750,921250,32011250,1563143750,58080093750,2719958906250,
%T 113913469531250,5214823539843750,228024893230468750,
%U 10704801509316406250,482674223446582031250,22664252188144042968750,1053427002068999511718750,49776941230938518066406250
%N a(n) = 5^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/5).
%F G.f.: Product_{k>=1} 1/(1 - 2*(25*x)^k)^(1/5).
%F a(n) ~ 50^n / (Gamma(1/5) * QPochhammer(1/2)^(1/5) * n^(4/5)).
%t nmax = 20; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
%t nmax = 20; CoefficientList[Series[Product[1/(1-2*(25*x)^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]
%Y Cf. A070933 (m=1), A370713 (m=2), A370715 (m=3), A370732 (m=4).
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Feb 28 2024