A155208 G.f.: A(x) = exp( Sum_{n>=1} (4^n + 1)^n * x^n/n ), a power series in x with integer coefficients.

1, 5, 157, 92285, 1091087581, 226287110093405, 788215837483128170845, 45292586018794926904179045725, 42540488665745908362239138191829777245, 649578584556365450465861374646071307864262693725

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 + 5*x + 157*x^2 + 92285*x^3 + 1091087581*x^4 +...
log(A(x)) = 5*x + 17^2*x^2/2 + 65^3*x^3/3 + 257^4*x^4/4 + 1025^5*x^5/5 +...
		

Crossrefs

Cf. A155207, A155209, A155210, variants: A155201, A155204.

Programs

PARI

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