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%I #6 May 16 2019 11:53:55
%S 1,3,11,47,217,1065,5453,28789,155633,857207,4793103,27136555,
%T 155249971,896133487,5212477023,30522169103,179777122393,
%U 1064411910393,6331361864657,37817265028841,226731778956181,1363993567341257,8231111557650837,49812263080757845
%N G.f.: (x/(1 - x)) * Product_{k>=1} ((1 + x^k)/(1 - x^k))^a(k).
%F G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} 2*A(x^(2*k-1))/(2*k - 1) + x^k/k).
%t a[n_] := a[n] = SeriesCoefficient[x/(1 - x) Product[((1 + x^k)/(1 - x^k))^a[k], {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 24}]
%t terms = 24; A[_] = 0; Do[A[x_] = x Exp[Sum[2 A[x^(2 k - 1)]/(2 k - 1) + x^k/k, {k, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A029856, A036249, A052829, A073075.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, May 16 2019
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