A163132 A trisection of A163129.

9, 180, 2070, 17775, 125865, 773766, 4260645, 21453975, 100250100, 439479198, 1822654251, 7198716870, 27221451885, 98988000120, 347428124352, 1180620288702, 3894719205510, 12501561121560, 39124469772495

Offset

2,1

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.

Links

G. C. Greubel, Table of n, a(n) for n = 2..1002

Example

G.f.: T_2(q) = 9*q^2 + 180*q^5 + 2070*q^8 + 17775*q^11 + 125865*q^14 + ...
Terms are divisible by 9:
T_2/9 = [1, 20, 230, 1975, 13985, 85974, 473405, 2383775, 11138900, ...].

Mathematica

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 *)

Prog

(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)}

Crossrefs

Cf. A163129, A163130 (T_0), A163131 (T_1), A058091, A038500.

Sequence in context: A358741 A034221 A034240 * A212704 A231726 A064332

Adjacent sequences: A163129 A163130 A163131 * A163133 A163134 A163135

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2009

Extensions

Comment corrected by Paul D. Hanna, Jul 24 2009

Status

approved