A206302 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{d|n} A(x^d)^(n/d).

1, 1, 2, 5, 15, 45, 147, 484, 1649, 5698, 20055, 71373, 256998, 933458, 3418160, 12601291, 46739440, 174281272, 652962532, 2456802244, 9279423954, 35170693226, 133726116806, 509926989456, 1949634581725, 7472405641631, 28704432909043, 110496066015970

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 45*x^5 + 147*x^6 +...
such that, by definition,
A(x) = 1 + x*A(x) + x^2*A(x)^2*A(x^2) + x^3*A(x)^3*A(x^3) + x^4*A(x)^4*A(x^2)^2*A(x^4) + x^5*A(x)^5*A(x^5) + x^6*A(x)^6*A(x^2)^3*A(x^3)^2*A(x^6) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*exp(sumdiv(m, d, (m/d)*subst(log(A), x, x^d +x*O(x^n)))))); polcoeff(A, n)}
for(n=0, 35, print1(a(n), ", "))

Crossrefs

Cf. A206301.

Sequence in context: A149907 A148355 A148356 * A149908 A149909 A149910

Adjacent sequences: A206299 A206300 A206301 * A206303 A206304 A206305

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2012

Status

approved