A206720 G.f.: A(x) = x/(1-x) o x/(1-x^3) o x/(1-x^5) o x/(1-x^7) o..., a composition of functions x/(1-x^(2*n-1)) for n=1,2,3,...

1, 1, 1, 2, 3, 5, 8, 13, 23, 38, 63, 105, 178, 300, 501, 849, 1431, 2405, 4044, 6812, 11491, 19361, 32621, 54946, 92646, 156118, 262964, 443200, 746933, 1258840, 2121343, 3575153, 6025323, 10154336, 17112673, 28839762, 48605300, 81913614, 138049346, 232655873

Offset: 1

Author

Paul D. Hanna, Feb 11 2012

Keywords

• nonn

Comments

Compositional transpose of A206721.

Examples

			G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 + 13*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) = F_1(x/(1-x^3)) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 +...
F_3(x) = F_2(x/(1-x^5)) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 +...
F_4(x) = x/(1-x) o x/(1-x^3) o x/(1-x^5) o x/(1-x^7); ...
		

Crossrefs

Cf. A206721, A136750.

Programs

PARI

{a(n)=local(A=x+x*O(x^n)); if(n<=0, 0, for(i=1, n, A=A/(1-A^(2*(n-i)+1))); polcoeff(A, n))}
for(n=1,45,print1(a(n),", "))