A198413 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n * A(x^n) * x^n/n ).

1, 1, 3, 11, 46, 205, 962, 4668, 23268, 118374, 612305, 3210348, 17023682, 91140496, 491968036, 2674572509, 14631157562, 80480706331, 444865534251, 2469826058736, 13766223517639, 77003660186990, 432131032213098, 2432230966070833, 13726899289265314

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 46*x^4 + 205*x^5 + 962*x^6 +...
where
log(A(x)) = A(x)*A(x)*x + A(x)^2*A(x^2)*x^2/2 + A(x)^3*A(x^3)*x^3/3 +...
more explicitly,
log(A(x)) = x + 5*x^2/2 + 25*x^3/3 + 133*x^4/4 + 716*x^5/5 + 3947*x^6/6 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^m+x*O(x^n))*(x*A+x*O(x^n))^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A198520.

Sequence in context: A151138 A151139 A301412 * A151140 A271959 A151141

Adjacent sequences: A198410 A198411 A198412 * A198414 A198415 A198416

Keyword

nonn

Author

Paul D. Hanna, Oct 26 2011

Status

approved