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

1,1

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 = 1..1001

Example

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

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 *)

Prog

(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)}

Crossrefs

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

Sequence in context: A230145 A343808 A125520 * A060869 A012491 A136328

Adjacent sequences: A163128 A163129 A163130 * A163132 A163133 A163134

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2009

Extensions

Comment corrected by Paul D. Hanna, Jul 24 2009

Status

approved