A112122 - OEIS

%I #6 Mar 14 2015 00:56:09

%S 1,11,11,11,11,11,11,11,11,11,11,11,10,10,10,10,10,10,10,10,10,10,9,7,

%T 7,7,7,7,7,7,7,7,6,10,11,11,11,11,11,11,11,11,10,2,7,1,1,1,1,1,1,1,11,

%U 1,10,1,3,3,3,3,3,3,2,2,10,11,11,3,3,3,3,3,2,6,9,5,3,2,4,4,4,4,3,5,11,6,7

%N Unique sequence of numbers {1,2,3,...,11} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (11th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

%e G.f.: A(x) = x + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 +...

%e then A(x) = B(B(B(B(B(B(B(B(B(B(B(x))))))))))) where

%e B(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 +...

%e is the g.f. of A112123.

%o (PARI) {a(n,m=11)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); G=F+x*O(x^n);for(i=1,m-1,G=subst(F,x,G)); return(polcoeff(G,n,x)))}

%Y Cf. A112123, A112104-A112121, A112124-A112127.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 27 2005