login
G.f.: A(x) = ...o x/(1-x^7) o x/(1-x^5) o x/(1-x^3) o x/(1-x), a composition of functions x/(1-x^(2*n-1)) for n=...3,2,1.
1

%I #7 Mar 30 2012 18:37:35

%S 1,1,1,2,5,12,28,65,155,387,1002,2641,7016,18743,50321,135608,366399,

%T 992221,2693705,7333666,20026582,54858122,150739957,415479332,

%U 1148563576,3183963911,8848963329,24650364462,68810859415,192439812663,539072534278,1512285566266

%N G.f.: A(x) = ...o x/(1-x^7) o x/(1-x^5) o x/(1-x^3) o x/(1-x), a composition of functions x/(1-x^(2*n-1)) for n=...3,2,1.

%C Compositional transpose of A206720.

%e G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 12*x^6 + 28*x^7 + 65*x^8 +...

%e where A(x) is the limit of composition of functions x/(1-x^(2*n-1)):

%e F_1(x) = x/(1-x)

%e F_2(x) = x/(1-x^3) o F_1(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 11*x^6 +...

%e F_3(x) = x/(1-x^5) o F_2(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 12*x^6 +...

%e F_4(x) = x/(1-x^7) o x/(1-x^5) o x/(1-x^3) o x/(1-x); ...

%o (PARI) {a(n)=local(A=x+x*O(x^n)); if(n<=0, 0, for(i=1, n, A=A/(1-A^(2*i-1))); polcoeff(A, n))}

%o for(n=1,45,print1(a(n),", "))

%Y Cf. A206720, A136751.

%K nonn

%O 1,4

%A _Paul D. Hanna_, Feb 11 2012