The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A186930 McKay-Thompson series of class 12c for the Monster group with a(0) = -4. 3
 1, -4, 5, 0, -5, 0, 9, 0, -14, 0, 19, 0, -34, 0, 55, 0, -69, 0, 104, 0, -164, 0, 209, 0, -283, 0, 413, 0, -539, 0, 712, 0, -968, 0, 1248, 0, -1642, 0, 2167, 0, -2731, 0, 3526, 0, -4592, 0, 5736, 0, -7244, 0, 9255, 0, -11520, 0, 14378, 0, -18018, 0, 22238, 0, -27556, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882). REFERENCES D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). LINKS Seiichi Manyama, Table of n, a(n) for n = -1..10000 J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc., 323 (1991), no. 2, 691-701. Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of (b(q) * c(q^2)^3) / (c(q) * c(q^4)^2 * b(q^4)) in powers of q where b(), c() are cubic AGM functions. Expansion of (1/q) * chi(q) * chi(-q)^5 * chi(q^3)^5 * chi(-q^3) in powers of q where chi() is a Ramanujan theta function. Expansion of (eta(q)^4 * eta(q^6)^9) / (eta(q^2)^3 * eta(q^3)^4 * eta(q^4) * eta(q^12)^5) in powers of q. Euler transform of period 12 sequence [ -4, -1, 0, 0, -4, -6, -4, 0, 0, -1, -4, 0, ...]. a(2*n) = 0 unless n=0. a(2*n - 1) = A058491(n). a(n) = A187045(n) unless n=0. - Michael Somos, Sep 05 2015 EXAMPLE G.f. = 1/q - 4 + 5*q - 5*q^3 + 9*q^5 - 14*q^7 + 19*q^9 - 34*q^11 + 55*q^13 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q, q^2] QPochhammer[ -q^3, q^6])^5 (QPochhammer[ -q, q^2] QPochhammer[ q^3, q^6]), {q, 0, n}]; (* Michael Somos, Sep 05 2015 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A)^4 * eta(x^6 + A)^9) / (eta(x^2 + A)^3 * eta(x^3 + A)^4 * eta(x^4 + A) * eta(x^12 + A)^5), n))}; CROSSREFS Cf. A058491, A187045. Sequence in context: A011286 A246927 A187045 * A159567 A164357 A092487 Adjacent sequences: A186927 A186928 A186929 * A186931 A186932 A186933 KEYWORD sign AUTHOR Michael Somos, Mar 07 2011 STATUS approved

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

Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)