A163131 A trisection of A163129.

3, 75, 969, 8964, 66975, 429096, 2442372, 12640320, 60454713, 270391857, 1141260315, 4578160257, 17554638039, 64642406670, 229486544439, 788018124312, 2624648438025, 8499852952224, 26820711864657, 82613109082410

Offset: 1

Author

Paul D. Hanna, Jul 21 2009

Keywords

• nonn

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.

Examples

			G.f.: T_1(q) = 3*q + 75*q^4 + 969*q^7 + 8964*q^10 + 66975*q^13 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A163129, A163130 (T_0), A163132 (T_2), A058091, A038500.

Programs

Mathematica

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 + 1];  Table[a[n], {n, 0, 50}]  (* G. C. Greubel, Jul 03 2018 *)

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)}

Extensions

Comment corrected by Paul D. Hanna, Jul 24 2009