A157675 G.f.: A(x) = exp( Sum_{n>=1} A(2^n*x)^n * x^n/n ).

1, 1, 3, 19, 237, 5741, 270857, 25099497, 4605241487, 1681614043919, 1225216121453227, 1783355695990213771, 5188617952349909215215, 30183911091753947571225583, 351131331387346570480797774119

Offset

0,3

Comments

Conjectured to consist entirely of integers.

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..14.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 237*x^4 + 5741*x^5 + 270857*x^6 +...
A(x) = exp(A(2x)*x + A(4x)^2*x^2/2 + A(8x)^3*x^3/3 + A(16x)^4*x^4/4 +...).

Prog

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

Crossrefs

Cf. A156907.

Sequence in context: A001929 A349962 A230316 * A355216 A135754 A340225

Adjacent sequences: A157672 A157673 A157674 * A157676 A157677 A157678

Keyword

nonn

Author

Paul D. Hanna, Mar 06 2009

Status

approved