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Search: id:A158110
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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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1
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| 1, 2, 130, 44739500, 4611686018516874838, 8507059173023461595807737228465099196, 17552048611426197782986337964292523732529439672780432120964458900
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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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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PROGRAM
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(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
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Cf. A155200.
Sequence in context: A003369 A099824 A098533 this_sequence A117626 A142251 A125633
Adjacent sequences: A158107 A158108 A158109 this_sequence A158111 A158112 A158113
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 19 2009
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