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Search: id:A161808
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| 1, 3, 3, 3, 9, 12, 12, 27, 36, 57, 141, 165, 135, 321, 450, 399, 780, 1068, 1308, 2913, 3537, 2736, 5940, 8430, 7173, 13251, 18267, 17661, 35007, 45051, 31866, 58506, 85890, 65694, 102000, 145293, 101547, 140574, 203781, 114765, 93051, 161754
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OFFSET
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0,2
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COMMENT
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A162552 forms the l.g.f. of log[ Sum_{n>=0} x^(n^2) ], and
A038500(n) is the highest power of 3 dividing n.
The first negative term is a(43) = -162729.
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EXAMPLE
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G.f.: A(q) = 1 + 3*q + 3*q^2 + 3*q^3 + 9*q^4 + 12*q^5 + 12*q^6 +...
log(A(q)) = 3*q - 3*q^2/2 + 9*q^3/3 + 9*q^4/4 - 12*q^5/5 + 45*q^6/6 - 18*q^7/7 +...
Compare to: q - q^2/2 + q^3/3 + 3*q^4/4 - 4*q^5/5 + 5*q^6/6 - 6*q^7/7 +...
which equals log( Sum_{n>=0} q^(n^2) ) as described by A162552.
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PROGRAM
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(PARI) {a(n)=local(Q=sum(m=0, n, x^(m^2))+x*O(x^n), A); A=exp(sum(k=1, n, polcoeff(log(Q), k)*3*3^valuation(k, 3)*x^k)+x*O(x^n)); polcoeff(A, n)}
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CROSSREFS
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Cf. A161804 (variant).
Sequence in context: A132171 A127975 A060828 this_sequence A160589 A097707 A115282
Adjacent sequences: A161805 A161806 A161807 this_sequence A161809 A161810 A161811
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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), Jul 21 2009
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