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E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/2)))^2.
2

%I #11 Sep 02 2024 08:38:42

%S 1,2,12,122,1780,34082,810740,23093562,767175972,29140904402,

%T 1246366394548,59292772664666,3106206974812292,177715679350850370,

%U 11026719500616041076,737552919428497318394,52907911316906095281508,4051998061642112552244722

%N E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/2)))^2.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052894.

%F E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (2 - exp(x))) )^2.

%F a(n) = (2/(n+2)!) * Sum_{k=0..n} (n+k+1)! * Stirling2(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(2-exp(x)))/x)^2))

%o (PARI) a(n) = 2*sum(k=0, n, (n+k+1)!*stirling(n, k, 2))/(n+2)!;

%Y Cf. A052894, A375898.

%Y Cf. A005649.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 01 2024