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%I #8 Mar 30 2024 02:33:24
%S 1,2,10,64,548,5608,68936,973600,15700352,283559424,5685644928,
%T 125227712256,3007981305600,78237291643392,2191215982262784,
%U 65744691667064832,2103999919044163584,71538799576401408000,2575460412946013810688,97868678834373255069696,3914776163575281528889344
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - 2*x^k/k).
%F a(n) ~ c * 2^n * n!, where c = Product_{k>=2} 1/(1 - 2^(1-k)/k) = 1.5345676172355916355224667976662106649465582052467986508967405417359... - _Vaclav Kotesovec_, Mar 28 2024
%t nmax = 20; CoefficientList[Series[Product[1/(1 - 2 x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007841, A371546, A371548.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 27 2024