A163130 - OEIS

%I #7 Jul 04 2018 08:57:51

%S 1,30,441,4431,35094,235053,1386027,7384578,36192519,165311094,

%T 710631279,2897149824,11270295093,42043460145,151025654781,

%U 524199355128,1763256696537,5762466306432,18337081016448,56926806819666

%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="/A163130/b163130.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: T_0(q) = 1 + 30*q^3 + 441*q^6 + 4431*q^9 + 35094*q^12 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 150; 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]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jul 03 2018 *)

%o (PARI) {a(n)=local(L=sum(m=1, 3*n, 3*sigma(m)*3^valuation(m, 3)*x^m/m)+x*O(x^(3*n))); polcoeff(exp(L), 3*n)}

%Y Cf. A163129, A163131 (T_1), A163132 (T_2), A058091.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 21 2009

%E Comment corrected by _Paul D. Hanna_, Jul 24 2009