A155204 G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients.

1, 4, 58, 7528, 11333974, 173018964568, 25223063625377572, 34295288559321731710864, 429734241619476967064512081894, 49292144502053186639397817183561560472

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 + 4*x + 58*x^2 + 7528*x^3 + 11333974*x^4 + 173018964568*x^5 +...
log(A(x)) = 4*x + 10^2*x^2/2 + 28*x^3/3 + 82^4*x^4/4 + 244^5*x^5/5 +...
		

Crossrefs

Cf. A155203, A155205, A155206, A155812 (triangle), A202989; variants: A155201, A155208.

Programs

PARI

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

Formula

Equals row sums of triangle A155812.