%I #10 Oct 06 2017 15:26:31

%S 1,1,4,28,264,2992,38496,544464,8298080,134500672,2297361024,

%T 41077857152,765073498368,14786330691072,295652808207360,

%U 6101427222041856,129707991377671680,2835915576534111232,63683889838128080896,1467174199736163264512,34643692576697214742528,837694231078769706999808,20727017363846896783998976

%N G.f. A(x) satisfies: A( 2*x - A(x) - x^2 ) = 2*x - A(x).

%H Paul D. Hanna, <a href="/A292810/b292810.txt">Table of n, a(n) for n = 1..200</a>

%F G.f.: x + G(x)^2 where x = G(x) - G(x)^2 - G(G(x))^2, and G(x) is the g.f. of A177409.

%e G.f.: A(x) = x + x^2 + 4*x^3 + 28*x^4 + 264*x^5 + 2992*x^6 + 38496*x^7 + 544464*x^8 + 8298080*x^9 + 134500672*x^10 + 2297361024*x^11 + 41077857152*x^12 + 765073498368*x^13 + 14786330691072*x^14 + 295652808207360*x^15 +...

%e such that A( 2*x - A(x) - x^2 ) = 2*x - A(x).

%o (PARI) {a(n) = my(A=x, V=[1, 1]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(G=A, x, 2*x - x^2 - A) )[#V]/(-1) ); V[n]}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A177409.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Sep 24 2017