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A163132 A trisection of A163129. 4
9, 180, 2070, 17775, 125865, 773766, 4260645, 21453975, 100250100, 439479198, 1822654251, 7198716870, 27221451885, 98988000120, 347428124352, 1180620288702, 3894719205510, 12501561121560, 39124469772495 (list; graph; refs; listen; history; text; internal format)
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: A304402 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

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Last modified January 18 05:06 EST 2022. Contains 350410 sequences. (Running on oeis4.)