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Search: id:A161806
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| 3, 30, 141, 513, 1815, 5727, 15882, 42417, 108165, 255831, 585258, 1302966, 2762349, 5705829, 11577633, 22708053, 43675938, 83011398, 153929484, 281210994, 509494515, 905832642, 1591395774, 2778237765, 4776943011
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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_1(q) = 3 + 30*q + 141*q^2 + 513*q^3 + 1815*q^4 + 5727*q^5 +...
Terms are divisible by 3:
A/3=[1,10,47,171,605,1909,5294,14139,36055,85277,195086,434322,...].
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PROGRAM
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(PARI) {a(n)=local(L=sum(m=1, 3*n+1, 3*3^valuation(m, 3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+1))); polcoeff(exp(L), 3*n+1)}
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CROSSREFS
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Cf. A161804, other trisections: A161805 (T_0), A161807 (T_2).
Sequence in context: A100259 A031205 A020874 this_sequence A003689 A127868 A002463
Adjacent sequences: A161803 A161804 A161805 this_sequence A161807 A161808 A161809
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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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