A181316 G.f.: A(x) = exp( Sum_{n>=1} 2*((3^n-1)/2)^(n-1)*x^n/n ).

1, 2, 6, 122, 32242, 85808250, 2130201408474, 487143290951349930, 1021074261736069185881850, 19547957495950654924427730234138, 3408841202663503254998708590894515413082

Offset

0,2

Comments

Conjecture: exp( Sum_{n>=1} (q-1)*((q^n-1)/(q-1))^(n-1)*x^n/n ) is an integer series for all integer q>1.

Links

Table of n, a(n) for n=0..10.

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 122*x^3 + 32242*x^4 +...
log(A(x)) = 2*x + 2*4^1*x^2/2 + 2*13^2*x^3/3 + 2*40^3*x^4/4 + 2*121^4*x^5/5 + 2*364^5*x^6/6 +...+ 2*A003462(n)^(n-1)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 2*((3^m-1)/2)^(m-1)*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A180606.

Sequence in context: A039716 A164955 A060001 * A101753 A288185 A359961

Adjacent sequences: A181313 A181314 A181315 * A181317 A181318 A181319

Keyword

nonn

Author

Paul D. Hanna, Oct 31 2010

Status

approved