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

1,1

Links

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

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).

Example

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 + ...

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 *)

Prog

(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)}

Crossrefs

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

Sequence in context: A295903 A362767 A141243 * A038749 A002699 A335349

Adjacent sequences: A163226 A163227 A163228 * A163230 A163231 A163232

Keyword

nonn

Author

Paul D. Hanna, Jul 26 2009

Status

approved