A193201 G.f.: A(x) = Sum_{n>=0} x^n / Product_{d|n} (1 - x^d)^(n/d).

1, 1, 2, 4, 9, 18, 39, 81, 170, 355, 748, 1576, 3334, 7054, 14935, 31591, 66732, 140708, 296379, 624389, 1317807, 2790095, 5930254, 12652077, 27071714, 58019282, 124377335, 266404590, 569755992, 1216513200, 2593884456, 5526424017, 11773433242

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 9*x^5 + 20*x^6 + 31*x^7 + ...
where:
A(x) = 1 + x/(1-x) + x^2/((1-x)^2*(1-x^2)) + x^3/((1-x)^3*(1-x^3)) + x^4/((1-x)^4*(1-x^2)^2*(1-x^4)) + x^5/((1-x)^5*(1-x^5)) + x^6/((1-x)^6*(1-x^2)^3*(1-x^3)^2*(1-x^6)) + ...

Prog

(PARI) {a(n)=local(A=1); A=1+sum(m=1, n, x^m/prod(d=1, m, if(m%d==0, (1-x^d +x*O(x^n))^(m/d), 1))); polcoeff(A, n)}

Crossrefs

Sequence in context: A036610 A219755 A289846 * A038044 A189911 A026732

Adjacent sequences: A193198 A193199 A193200 * A193202 A193203 A193204

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved