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a(n) = 4^n * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/4).
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%I #7 Feb 29 2024 06:24:01

%S 1,2,18,108,822,4796,37492,231704,1738150,11857004,87262684,617409128,

%T 4638712124,33724007896,253800160808,1894353653552,14350905612038,

%U 108412437326412,827441075006796,6308125533133896,48388714839180756,371391625244862600,2860885559165073624

%N a(n) = 4^n * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/4).

%F G.f.: Product_{k>=1} 1/(1 - 2*(4*x)^k)^(1/4).

%F a(n) ~ 8^n / (Gamma(1/4) * QPochhammer(1/2)^(1/4) * n^(3/4)).

%t nmax = 30; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 4^Range[0, nmax]

%t nmax = 30; CoefficientList[Series[Product[1/(1-2*(4*x)^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]

%Y Cf. A070933 (m=1), A370713 (m=2), A370715 (m=3), A370733 (m=5).

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 28 2024