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 A058532 McKay-Thompson series of class 18B for the Monster group. 3
 1, 0, 7, 10, 27, 38, 82, 108, 207, 278, 486, 644, 1052, 1404, 2182, 2880, 4293, 5654, 8182, 10692, 15076, 19604, 27108, 35000, 47547, 61020, 81713, 104236, 137781, 174800, 228498, 288360, 373174, 468566, 601020, 751036, 955642, 1188756, 1501730, 1859944 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = -1..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA From Michael Somos, Aug 19 2012: (Start) Expansion of -2 + (1/q) * psi(q^3)^2 / (psi(q) * phi(q^9)) * (f(-q^3)^2 / (f(-q) * f(-q^9)))^3 in powers of q where psi(), f() are Ramanujan theta functions. Expansion of -3 + (1/q) * (chi(-q^9) / chi(-q))^3 + q * (chi(-q) / chi(-q^9))^3 in powers of q where chi() is a Ramanujan theta function. Expansion of -2 + (eta(q^3) * eta(q^6))^4 / (eta(q) * eta(q^2) * eta(q^9) * eta(q^18))^2 in powers of q. Expansion of -5 + (eta(q^3)^8 + 4 * eta(q^6)^8) /(eta(q) * eta(q^2) * eta(q^3)^2 * eta(q^6)^2 * eta(q^9) * eta(q^18)). a(n) = A215407(n) unless n=0. (End) a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Sep 10 2015 EXAMPLE T18B = 1/q + 7*q + 10*q^2 + 27*q^3 + 38*q^4 + 82*q^5 + 108*q^6 + 207*q^7 + ... MATHEMATICA QP = QPochhammer; s = -2*q+(QP[q^3]*QP[q^6])^4/(QP[q]*QP[q^2]*QP[q^9]* QP[q^18])^2 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, after 3rd formula *) PROG (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); A = eta(x + A) * eta(x^2 + A) / (eta(x^9 + A) * eta(x^18 + A)); polcoeff( x + A + 9 * x^2 / A, n))} /* Michael Somos, Aug 19 2012 */ CROSSREFS Cf. A000521, A007240, A007241, A007267, A014708, A045478. Cf. A093073, A123676, A128517, A215407. Sequence in context: A064948 A064950 A240795 * A280966 A174466 A070422 Adjacent sequences:  A058529 A058530 A058531 * A058533 A058534 A058535 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2000 STATUS approved

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Last modified September 29 14:39 EDT 2020. Contains 337432 sequences. (Running on oeis4.)