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A158110
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G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ).
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OFFSET
| 0,2
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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.
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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 +...
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PROG
| (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^3)*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
| Cf. A155200.
Sequence in context: A099824 A190578 A098533 * A117626 A142251 A125633
Adjacent sequences: A158107 A158108 A158109 * A158111 A158112 A158113
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 19 2009
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