A158053 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x*A(x))^n * x^n/n ).

1, 1, 3, 9, 37, 183, 1175, 10405, 132911, 2533697, 70988149, 2886198771, 168860266189, 14046492509383, 1668792185650203, 280222608364043833, 66930106539423614233, 22572046654805538142763

Offset

0,3

Comments

Compare to: M(x) = exp( Sum_{n>=1} (1 + x*M(x))^n * x^n/n ) where M(x) is the g.f. of the Motzkin numbers (A001006).

Links

Table of n, a(n) for n=0..17.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 37*x^4 + 183*x^5 + 1175*x^6 +...
log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 105*x^4/4 + 671*x^5/5 + 5525*x^6/6 +...
log(A(x)) = (1+2x*A(x))*x + (1+4x*A(x))^2*x^2/2 + (1+8x*A(x))^3*x^3/3 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (1+2^m*x*A)^m*x^m/m+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Cf. A156214.

Sequence in context: A321734 A008986 A105215 * A009179 A030819 A030904

Adjacent sequences: A158050 A158051 A158052 * A158054 A158055 A158056

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2009

Status

approved