This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A112143 McKay-Thompson series of class 8D for the Monster group. 6
 1, -4, 2, 8, -1, -20, -2, 40, 3, -72, 2, 128, -4, -220, -4, 360, 5, -576, 8, 904, -8, -1384, -10, 2088, 11, -3108, 12, 4552, -15, -6592, -18, 9448, 22, -13392, 26, 18816, -29, -26216, -34, 36224, 38, -49700, 42, 67728, -51, -91688, -56, 123392, 66, -165128, 78, 219784, -85, -291072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The convolution square of this sequence is A007248, except for the constant term: T8D(q)^2 = T4C(q^2) - 8. - G. A. Edgar, Apr 02 2017 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..499 from G. A. Edgar) D. Alexander, C. Cummins, J. McKay and C. Simons, Completely Replicable Functions, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy. D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). FORMULA Expansion of q^(1/2)*(eta(q) / eta(q^4))^4 in powers of q. - G. A. Edgar, Apr 02 2017 a(0) = 1, a(n) = -(4/n)*Sum_{k=1..n} A046897(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 28 2017 EXAMPLE T8D = 1/q -4*q +2*q^3 +8*q^5 -q^7 -20*q^9 -2*q^11 +40*q^13 +... MATHEMATICA eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]/eta[q^4])^4, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 10 2018 *) PROG (PARI) q='q+O('q^50); Vec((eta(q)/eta(q^4))^4) \\ G. C. Greubel, May 10 2018 CROSSREFS Cf. A007248, A046897. Sequence in context: A029841 * A112151 A112152 A211883 A083489 A065464 Adjacent sequences:  A112140 A112141 A112142 * A112144 A112145 A112146 KEYWORD sign 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 18 12:02 EDT 2018. Contains 312737 sequences. (Running on oeis4.)