A128326 - OEIS

%I #7 Dec 20 2014 22:24:40

%S 1,1,3,12,57,305,1787,11269,75629,535960,3987913,31021693,251445581,

%T 2117993712,18499513147,167246537937,1562556275281,15066167302802,

%U 149737897716757,1532313152898208,16129331500727047

%N G.f.: A(x) = 1 + G(G(G(x))), where G(x) = x + x*G(G(x)) is the g.f. of A030266.

%C Equals row 1 of table A128325.

%F G.f. satisfies: A(x) = x/(1 - A( x/(1 - A(x)) )) when offset is taken to be 1. - _Paul D. Hanna_, Dec 20 2014

%o (PARI) {a(n)=local(A=1+x,B);for(i=0,n,A = 1 + x*A * subst(A,x,x*A+x*O(x^n))); B=A;B=subst(B,x,x*A+x*O(x^n));polcoeff(B,n)}

%o for(n=0, 30, print1(a(n), ", "))

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A = 1/subst(1-x*A, x, x/(1-x*A +x*O(x^n))) ); polcoeff(A, n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A030266; A128325 (table), A128327 (row 2), A128328 (row 3), A128329 (main diagonal).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 11 2007