# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a112320 Showing 1-1 of 1 %I A112320 #10 Oct 04 2024 16:37:32 %S A112320 1,3,12,70,560,5810,74760,1153740,20817588,430604724,10052947476, %T A112320 261595087182,7509722346204,235808741944100,8040824716606176, %U A112320 295914258931377276,11690732617035570008,493527339623630078552 %N A112320 Coefficient of x^n in the (n+1)-th iteration of (x + x^2) for n>=1. %F A112320 a(n) = [x^n] F_{n+1}(x) where F_{n+1}(x) = F_n(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1. %e A112320 The first few iterations of (x+x^2) begin: %e A112320 F(x) = x + x^2; %e A112320 F(F(x)) = (1)*x + 2*x^2 + 2*x^3 + x^4; %e A112320 F(F(F(x))) = x + (3)*x^2 + 6*x^3 + 9*x^4 + 10*x^5 +...; %e A112320 F(F(F(F(x)))) = x + 4*x^2 + (12)*x^3 + 30*x^4 + 64*x^5 +...; %e A112320 F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + (70)*x^4 + 220*x^5 +...; %e A112320 F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + (560)*x^5 +...; %e A112320 coefficients enclosed in parenthesis form the initial terms of this sequence. %o A112320 (PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^n));if(n<1,0, for(i=1,n+1,G=subst(F,x,G));return(polcoeff(G,n,x)))} %o A112320 for(n=1,25,print1(a(n),", ")) %Y A112320 Cf. A112317, A112319. %K A112320 nonn %O A112320 1,2 %A A112320 _Paul D. Hanna_, Sep 06 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE