A163228 A bisection of A162584.

1, 8, 50, 240, 1024, 3888, 13696, 44960, 139970, 414904, 1181568, 3242928, 8623104, 22268752, 56039936, 137686048, 331039232, 780029536, 1804321074, 4102056144, 9177497600, 20225408480, 43948974720, 94236510112, 199549448704

Offset

0,2

Links

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

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_0(q) = 1 + 8*q^2 + 50*q^4 + 240*q^6 + 1024*q^8 + 3888*q^10 + ...
Bisection B_1(q) of A162584 begins:
B_1(q) = 2*q + 16*q^3 + 96*q^5 + 448*q^7 + 1858*q^9 + 6896*q^11 + ...

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

Prog

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

Crossrefs

Cf. A162584, A163229 (B_1), A029839 (T16B).

Sequence in context: A212063 A300318 A290617 * A033463 A030279 A133357

Adjacent sequences: A163225 A163226 A163227 * A163229 A163230 A163231

Keyword

nonn

Author

Paul D. Hanna, Jul 26 2009

Status

approved