A192634 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n*A(x^n + x^(2*n))/n ).

1, 1, 2, 5, 15, 50, 191, 789, 3566, 17306, 89871, 496250, 2901931, 17901455, 116129282, 789973067, 5620945352, 41739598787, 322802306649, 2595133213658, 21650633864406, 187146890460633, 1673639663735620, 15464023782414504, 147441877065741283

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..24.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 50*x^5 + 191*x^6 +...
The g.f. satisfies:
log(A(x)) = x*A(x+x^2) + x^2*A(x^2+x^4)/2 + x^3*A(x^3+x^6)/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+x^(2*m)+x*O(x^n))/m))); polcoeff(A, n)}

Crossrefs

Cf. A192635, A000081.

Sequence in context: A245311 A148367 A306836 * A350490 A304386 A140639

Adjacent sequences: A192631 A192632 A192633 * A192635 A192636 A192637

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2011

Status

approved