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E.g.f. satisfies A(x) = 1 + x*A(x)^3*(exp(x*A(x)) - 1).
2

%I #9 Mar 11 2024 08:29:42

%S 1,0,2,3,100,545,17946,203497,7194440,132963777,5172409630,

%T 135827977241,5868623306844,200952952956769,9665278822378466,

%U 407661518051710665,21789972653746494736,1088515671895571005313,64406426353877958253254

%N E.g.f. satisfies A(x) = 1 + x*A(x)^3*(exp(x*A(x)) - 1).

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

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

%Y Cf. A370988, A371115, A371119.

%Y Cf. A371122.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 11 2024