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%I #8 Jul 04 2018 08:58:13
%S 9,180,2070,17775,125865,773766,4260645,21453975,100250100,439479198,
%T 1822654251,7198716870,27221451885,98988000120,347428124352,
%U 1180620288702,3894719205510,12501561121560,39124469772495
%N A trisection of A163129.
%C A163129 is defined by the g.f.:
%C A(q) = exp( Sum_{n>=1} sigma(n) * 3*A038500(n) * q^n/n ),
%C where A038500(n) = highest power of 3 dividing n.
%C Trisections are related by: A(q) = T_0(q) + T_1(q) + T_2(q) where
%C 3*T_0(q)/T_1(q) = 3*T_1(q)/T_2(q) = T9B(q), the g.f. of A058091,
%C which is the McKay-Thompson series of class 9B for Monster.
%H G. C. Greubel, <a href="/A163132/b163132.txt">Table of n, a(n) for n = 2..1002</a>
%e G.f.: T_2(q) = 9*q^2 + 180*q^5 + 2070*q^8 + 17775*q^11 + 125865*q^14 + ...
%e Terms are divisible by 9:
%e T_2/9 = [1, 20, 230, 1975, 13985, 85974, 473405, 2383775, 11138900, ...].
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 250; a[n_]:= SeriesCoefficient[ Series[Exp[Sum[DivisorSigma[1, k]*3^(IntegerExponent[k, 3] + 1)*q^k/k, {k, 1, 3*nmax + 1}]], {q, 0, nmax}], 3*n + 2]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jul 03 2018 *)
%o (PARI) {a(n)=local(L=sum(m=1, 3*n+2, 3*sigma(m)*3^valuation(m, 3)*x^m/m)+x*O(x^(3*n+2))); polcoeff(exp(L), 3*n+2)}
%Y Cf. A163129, A163130 (T_0), A163131 (T_1), A058091, A038500.
%K nonn
%O 2,1
%A _Paul D. Hanna_, Jul 21 2009
%E Comment corrected by _Paul D. Hanna_, Jul 24 2009
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