A155205 G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n * x^n/n ), a power series in x with integer coefficients.

1, 2, 34, 5924, 10252294, 166020197708, 24810918565918804, 34076399079565985138408, 428687477154543524080261047622, 49247086840315416213775472777558582540

Offset: 0

Author

Paul D. Hanna, Feb 04 2009

Keywords

• nonn

Comments

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

Examples

			G.f.: A(x) = 1 + 2*x + 34*x^2 + 5924*x^3 + 10252294*x^4 +...
log(A(x)) = 2*x + 8^2*x^2/2 + 26^3*x^3/3 + 80^4*x^4/4 + 242^5*x^5/5 +...
		

Crossrefs

Cf. A060613, A155203, A155204, A155206, A155812 (triangle), variants: A155202, A155209.

Programs

PARI

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