A206721 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, 1, 1, 2, 5, 12, 28, 65, 155, 387, 1002, 2641, 7016, 18743, 50321, 135608, 366399, 992221, 2693705, 7333666, 20026582, 54858122, 150739957, 415479332, 1148563576, 3183963911, 8848963329, 24650364462, 68810859415, 192439812663, 539072534278, 1512285566266

Offset: 1

Author

Paul D. Hanna, Feb 11 2012

Keywords

• nonn

Comments

Compositional transpose of A206720.

Examples

			G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 12*x^6 + 28*x^7 + 65*x^8 +...
where A(x) is the limit of composition of functions x/(1-x^(2*n-1)):
F_1(x) = x/(1-x)
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 +...
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 +...
F_4(x) = x/(1-x^7) o x/(1-x^5) o x/(1-x^3) o x/(1-x); ...
		

Crossrefs

Cf. A206720, A136751.

Programs

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))}
for(n=1,45,print1(a(n),", "))