A193200 G.f.: A(x) = Sum_{n>=0} x^n * Product_{d|n} (1 + x^d)^(n/d).

1, 1, 2, 3, 6, 10, 17, 32, 54, 92, 170, 311, 555, 986, 1756, 3100, 5370, 9295, 16552, 30535, 57564, 108830, 202947, 369829, 659380, 1162254, 2053619, 3675529, 6683060, 12293599, 22697283, 41734139, 76077655, 137460434, 247056655, 444239896, 803916709

Offset

0,3

Links

Table of n, a(n) for n=0..36.

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: A123908 A233268 A026397 * A026779 A081028 A325232

Adjacent sequences: A193197 A193198 A193199 * A193201 A193202 A193203

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved