A155210 G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients.

1, 3, 42, 9378, 39179127, 2766569881269, 3234201150559172040, 62076685218110095082936700, 19446778350632942283719042004313725, 98999235365955012033013202024947235500115415

Offset: 0

Author

Paul D. Hanna, Feb 04 2009

Keywords

• nonn

Comments

More generally, for m integer, exp( Sum_{n>=1} (m^n - 1)^n/(m-1)^(n-1) * x^n/n ) is a power series in x with integer coefficients.

Note that g.f. exp( Sum_{n>=1} (4^n - 1)^n/3^n * x^n/n ) has fractional coefficients as a power series in x.

Examples

			G.f.: A(x) = 1 + 3*x + 42*x^2 + 9378*x^3 + 39179127*x^4 +...
log(A(x)) = 3*x + 15^2/3*x^2/2 + 63^3/3^2*x^3/3 + 255^4/3^3*x^4/4 +...
		

Crossrefs

Cf. A155207, A155208, A155209, variant: A155206.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n+1,(4^m-1)^m/3^(m-1)*x^m/m)+x*O(x^n)),n)}