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A158110 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ). 2
1, 2, 130, 44739500, 4611686018516874838, 8507059173023461595807737228465099196, 17552048611426197782986337964292523732529439672780432120964458900 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 19 2009
STATUS
approved

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)