A158110 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ).

1, 2, 130, 44739500, 4611686018516874838, 8507059173023461595807737228465099196, 17552048611426197782986337964292523732529439672780432120964458900

Offset

0,2

Comments

Conjecture: given q and m are nonnegative integers, then

exp( Sum_{n>=1} q^(n^m)*x^n/n )

is a power series in x with integer coefficients.

Links

Table of n, a(n) for n=0..6.

Example

G.f.: A(x) = 1 + 2*x + 130*x^2 + 44739500*x^3 +...
log(A(x)) = 2*x + 2^8*x^2/2 + 2^27*x^3/3 + 2^64*x^4/4 +...

Prog

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

Crossrefs

Cf. A155200.

Sequence in context: A218434 A354054 A303445 * A117626 A084549 A142251

Adjacent sequences: A158107 A158108 A158109 * A158111 A158112 A158113

Keyword

nonn

Author

Paul D. Hanna, Mar 19 2009

Status

approved