|
|
A159593
|
|
G.f.: A(x) = exp( Sum_{n>=1} A(3^n*x)^n * x^n/n ).
|
|
0
|
|
|
1, 1, 4, 49, 1768, 187474, 58888462, 55210937881, 155033790773008, 1305338879106660550, 32966118096763299572020, 2497521410388697783376754490, 567627952695201383291867693446222
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Compare to: C(x) = exp( Sum_{n>=1} C(x)^n*x^n/n ) where C(x) = g.f. of Catalan numbers (A000108).
|
|
LINKS
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 + x + 4*x^2 + 49*x^3 + 1768*x^4 + 187474*x^5 +...
log(A(x)) = x + 7*x^2/2 + 136*x^3/3 + 6859*x^4/4 + 927856*x^5/5 +...
log(A(x)) = A(3x)*x + A(9x)^2*x^2/2 + A(27x)^3*x^3/3 + A(81x)^4*x^4/4 +...
|
|
PROG
|
(PARI) {a(n)=local(A=1+x); for(n=2, n, A=exp(sum(k=1, n, subst(A, x, 3^k*x+x*O(x^n))^k*x^k/k))); polcoeff(A, n)}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|