|
|
A158053
|
|
G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x*A(x))^n * x^n/n ).
|
|
0
|
|
|
1, 1, 3, 9, 37, 183, 1175, 10405, 132911, 2533697, 70988149, 2886198771, 168860266189, 14046492509383, 1668792185650203, 280222608364043833, 66930106539423614233, 22572046654805538142763
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|