login
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) + ... ).
1

%I #5 May 26 2023 08:51:00

%S 1,1,3,10,37,154,676,3053,14187,67459,326241,1599480,7933272,39736160,

%T 200700204,1021052197,5227501077,26912956631,139244637915,

%U 723631840568,3775598797694,19770494002049,103865161431895,547291750362216,2891718659119578,15317429567883000

%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 = 26; 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, A045648, A363293.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 26 2023