This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A112173 McKay-Thompson series of class 36b for the Monster group. 2
 1, 2, 1, 4, 8, 6, 10, 16, 18, 26, 33, 40, 58, 74, 82, 112, 147, 166, 212, 268, 316, 392, 476, 560, 695, 838, 967, 1184, 1430, 1648, 1970, 2352, 2731, 3236, 3803, 4404, 5206, 6080, 6984, 8192, 9553, 10942, 12709, 14736, 16886, 19506, 22448, 25648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution square of A112206. - Vaclav Kotesovec, Sep 08 2015 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). FORMULA a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2015 Expansion of q^(1/3)*((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)*eta(q^4)* eta(q^12)))^2 in powers of q. - G. C. Greubel, Jun 16 2018 Expansion of abs(q^(1/3)*(eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^2) in powers of q. - G. C. Greubel, Jun 16 2018 EXAMPLE T36b = 1/q +2*q^2 +q^5 +4*q^8 +8*q^11 +6*q^14 +10*q^17 +... MATHEMATICA nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *) eta[q_]:= q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/3)*((eta[q^2]*eta[q^6])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^12]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *) PROG (PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)* eta(q^4)*eta(q^12)))^2; Vec(A) \\ G. C. Greubel, Jun 16 2018 CROSSREFS Cf. A112206. Sequence in context: A158451 A257706 A118272 * A058543 A156817 A008301 Adjacent sequences:  A112170 A112171 A112172 * A112174 A112175 A112176 KEYWORD nonn AUTHOR Michael Somos, Aug 28 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 07:07 EDT 2019. Contains 328292 sequences. (Running on oeis4.)