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

Author

Paul D. Hanna, Oct 31 2010

Keywords

• nonn

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.

Examples

			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 +...
		

Crossrefs

Cf. A180606.

Programs

PARI

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