A163130 A trisection of A163129.

1, 30, 441, 4431, 35094, 235053, 1386027, 7384578, 36192519, 165311094, 710631279, 2897149824, 11270295093, 42043460145, 151025654781, 524199355128, 1763256696537, 5762466306432, 18337081016448, 56926806819666

Offset: 0

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_0(q) = 1 + 30*q^3 + 441*q^6 + 4431*q^9 + 35094*q^12 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A163129, A163131 (T_1), A163132 (T_2), A058091.

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

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)}

Extensions

Comment corrected by Paul D. Hanna, Jul 24 2009