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%I #7 May 26 2023 08:50:56
%S 1,1,2,7,26,101,412,1756,7692,34350,155980,718312,3345890,15735091,
%T 74613107,356348561,1712593184,8276207120,40192085383,196045684833,
%U 960042529894,4718201036195,23263440797758,115042992517035,570463195069614,2835840294969867,14129895469191476
%N G.f. A(x) satisfies: A(x) = x * exp( A(x)^2/x - A(-x^2)^2/(2*x^2) + A(x^3)^2/(3*x^3) - A(-x^4)^2/(4*x^4) + ... ).
%t nmax = 27; A[_] = 0; Do[A[x_] = x Exp[-Sum[A[-(-x)^k]^2/(k (-x)^k), {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A005750, A005754, A049075, A363294.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 26 2023