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

0,2

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.

Links

Table of n, a(n) for n=0..9.

Example

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 +...

Prog

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

Crossrefs

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

Sequence in context: A156134 A183263 A369397 * A321529 A156486 A208170

Adjacent sequences: A155205 A155206 A155207 * A155209 A155210 A155211

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2009

Status

approved