A155206 G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n/2^(n-1) * x^n/n ), a power series in x with integer coefficients.

1, 2, 18, 1498, 1283090, 10377556482, 775351592888722, 532444511048570910746, 3349121447720205394546014978, 192371436319107536207473420480152034, 100642626897912335112447860229547933463000450

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} (3^n - 1)^n/2^n * x^n/n ) has fractional coefficients as a power series in x.

Examples

			G.f.: A(x) = 1 + 2*x + 18*x^2 + 1498*x^3 + 1283090*x^4 + 10377556482*x^5 +...
log(A(x)) = 2*x + 8^2/2*x^2/2 + 26^3/2^2*x^3/3 + 80^4/2^3*x^4/4 + 242^5/2^4*x^5/5 +...
		

Crossrefs

Cf. A155203, A155204, A155205, A155812 (triangle), variant: A155210.

Programs

PARI

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