A192635 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n*A(x^n/(1-x^n))/n ).

1, 1, 2, 5, 16, 57, 234, 1045, 5103, 26791, 150492, 898497, 5676600, 37797128, 264348852, 1936248546, 14814452947, 118126621277, 979597024690, 8432780717866, 75227768490441, 694375113431739, 6622156995890563, 65166502098671053

Offset

0,3

Comments

Compare to g.f. G(x) of A000081 (number of rooted trees with n nodes), which satisfies: G(x) = exp( Sum_{n>=1} x^n*G(x^n)/n ).

Links

Table of n, a(n) for n=0..23.

Example

G.f.: A(x) =  1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 57*x^5 + 234*x^6 +...
The g.f. A(x) satisfies:
log(A(x)) = x*A(x/(1-x)) + x^2*A(x^2/(1-x^2))/2 + x^3*A(x^3/(1-x^3))/3 +...

Prog

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

Crossrefs

Cf. A191412, A192634, A000081.

Sequence in context: A114296 A121689 A357580 * A009225 A157612 A348103

Adjacent sequences: A192632 A192633 A192634 * A192636 A192637 A192638

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2011

Status

approved