A159593 G.f.: A(x) = exp( Sum_{n>=1} A(3^n*x)^n * x^n/n ).

1, 1, 4, 49, 1768, 187474, 58888462, 55210937881, 155033790773008, 1305338879106660550, 32966118096763299572020, 2497521410388697783376754490, 567627952695201383291867693446222

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

Table of n, a(n) for n=0..12.

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

Cf. A157675.

Sequence in context: A129419 A212130 A049503 * A263441 A067717 A067714

Adjacent sequences: A159590 A159591 A159592 * A159594 A159595 A159596

Keyword

nonn

Author

Paul D. Hanna, May 02 2009

Status

approved