cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A163130 A trisection of A163129.

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%I A163130 #7 Jul 04 2018 08:57:51
%S A163130 1,30,441,4431,35094,235053,1386027,7384578,36192519,165311094,
%T A163130 710631279,2897149824,11270295093,42043460145,151025654781,
%U A163130 524199355128,1763256696537,5762466306432,18337081016448,56926806819666
%N A163130 A trisection of A163129.
%C A163130 A163129 is defined by the g.f.:
%C A163130 A(q) = exp( Sum_{n>=1} sigma(n) * 3*A038500(n) * q^n/n ),
%C A163130 where A038500(n) = highest power of 3 dividing n.
%C A163130 Trisections are related by: A(q) = T_0(q) + T_1(q) + T_2(q) where
%C A163130 3*T_0(q)/T_1(q) = 3*T_1(q)/T_2(q) = T9B(q), the g.f. of A058091,
%C A163130 which is the McKay-Thompson series of class 9B for Monster.
%H A163130 G. C. Greubel, <a href="/A163130/b163130.txt">Table of n, a(n) for n = 0..1000</a>
%e A163130 G.f.: T_0(q) = 1 + 30*q^3 + 441*q^6 + 4431*q^9 + 35094*q^12 + ...
%t A163130 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 A163130 (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 A163130 Cf. A163129, A163131 (T_1), A163132 (T_2), A058091.
%K A163130 nonn
%O A163130 0,2
%A A163130 _Paul D. Hanna_, Jul 21 2009
%E A163130 Comment corrected by _Paul D. Hanna_, Jul 24 2009