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Search: id:A161807
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| 3, 27, 111, 378, 1356, 4131, 10881, 29106, 73500, 167643, 382053, 849339, 1754061, 3605094, 7330311, 14094945, 26980563, 51481332, 93965784, 170910270, 311155296, 545970024, 955201653, 1676274750, 2849709768, 4831999623
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OFFSET
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0,1
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COMMENT
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G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),
where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and
A038500(n) is the highest power of 3 dividing n.
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EXAMPLE
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G.f.: T_2(q) = 3 + 27*q + 111*q^2 + 378*q^3 + 1356*q^4 + 4131*q^5 +...
Terms are divisible by 3:
A/3=[1,9,37,126,452,1377,3627,9702,24500,55881,127351,283113,...].
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PROGRAM
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(PARI) {a(n)=local(L=sum(m=1, 3*n+2, 3*3^valuation(m, 3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+2))); polcoeff(exp(L), 3*n+2)}
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CROSSREFS
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Cf. A161804, other trisections: A161805 (T_0), A161806 (T_1).
Sequence in context: A166102 A045491 A127210 this_sequence A063263 A034200 A080424
Adjacent sequences: A161804 A161805 A161806 this_sequence A161808 A161809 A161810
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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 20 2009
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