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3, 75, 969, 8964, 66975, 429096, 2442372, 12640320, 60454713, 270391857, 1141260315, 4578160257, 17554638039, 64642406670, 229486544439, 788018124312, 2624648438025, 8499852952224, 26820711864657, 82613109082410
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A163129 is defined by the g.f.:
A(q) = exp( Sum_{n>=1} sigma(n) * 3*A038500(n) * q^n/n ),
where A038500(n) = highest power of 3 dividing n.
Trisections are related by: A(q) = T_0(q) + T_1(q) + T_2(q) where
3*T_0(q)/T_1(q) = 3*T_1(q)/T_2(q) = T9B(q), the g.f. of A058091,
which is the McKay-Thompson series of class 9B for Monster.
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EXAMPLE
| G.f.: T_1(q) = 3*q + 75*q^4 + 969*q^7 + 8964*q^10 + 66975*q^13 +...
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PROG
| (PARI) {a(n)=local(L=sum(m=1, 3*n+1, 3*sigma(m)*3^valuation(m, 3)*x^m/m)+x*O(x^(3*n+1))); polcoeff(exp(L), 3*n+1)}
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CROSSREFS
| Cf. A163129, A163130 (T_0), A163132 (T_2), A058091, A038500.
Sequence in context: A093183 A189805 A125520 * A060869 A012491 A136328
Adjacent sequences: A163128 A163129 A163130 * A163132 A163133 A163134
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 21 2009
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EXTENSIONS
| Comment corrected by Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2009
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