A162286 G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{d|n} A(n*x/d)^d/d]*x^n ).

1, 1, 3, 10, 43, 232, 1658, 16041, 214998, 4034263, 106718470, 3996978281, 212525227794, 16073873629022, 1731645876520667, 265992096914842633, 58303791955275494006, 18248056245233786876850, 8159322089091615235254206

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

G.f. satisfies: A(x) = 1/Product{k>=1} (1 - x^k*A(k*x)). - Paul D. Hanna, Jul 01 2009

Example

G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 43*x^4 + 232*x^5 + 1658*x^6 + ...
log(A(x)) = A(x)*x + [A(2x) + A(x)^2/2]*x^2 + [A(3x) + A(x)^3/3]*x^3 + [A(4x) + A(2x)^2/2 + A(x)^4/4]*x^4 + ...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sumdiv(m, d, m*subst(A, x, m*x/d+x*O(x^n))^d/d)*x^m/m))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, 1-x^k*subst(A, x, k*x+x*O(x^n)))); polcoeff(A, n)} \\ Paul D. Hanna, Jul 01 2009

Crossrefs

Sequence in context: A006932 A001040 A181949 * A032269 A179501 A041737

Adjacent sequences: A162283 A162284 A162285 * A162287 A162288 A162289

Keyword

nonn

Author

Paul D. Hanna, Jun 29 2009

Status

approved