A163229 A bisection of A162584.

2, 16, 96, 448, 1858, 6896, 23776, 76608, 234432, 684336, 1921472, 5206208, 13679490, 34941120, 87036576, 211822976, 504784704, 1179589728, 2707337056, 6109982400, 13575320320, 29721857904, 64184237216, 136816242816

Offset: 1

Author

Paul D. Hanna, Jul 26 2009

Keywords

• nonn

Examples

			G.f.: B_1(q) = 2*q + 16*q^3 + 96*q^5 + 448*q^7 + 1858*q^9 + 6896*q^11 + ...
Bisection B_0(q) of A162584 begins:
B_0(q) = 1 + 8*q^2 + 50*q^4 + 240*q^6 + 1024*q^8 + 3888*q^10 + ...
		

Links

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

Crossrefs

Cf. A162584, A163228 (B_0), A029839 (T16B).

Programs

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax =250; a[n_]:= SeriesCoefficient[ Series[Exp[Sum[DivisorSigma[1, k]*2^(IntegerExponent[k, 2] + 1)*q^k/k, {k, 1, nmax}]], {q, 0, nmax}], 2*n + 1];  Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jul 03 2018 *)

PARI

{a(n)=local(L=sum(m=1, 2*n+1, 2*sigma(m)*2^valuation(m, 2)*x^m/m)+O(x^(2*n+2))); polcoeff(exp(L), 2*n+1)}

Formula

Define series bisections B_0(q) and B_1(q) of A162584, then

2*B_0(q)/B_1(q) = T16B(q) = q*eta(q^8)^6/(eta(q^4)^2*eta(q^16)^4),

the McKay-Thompson series of class 16B for the Monster group (A029839).