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 A058569 McKay-Thompson series of class 22a for Monster. 1
 1, 3, 4, 11, 17, 31, 45, 71, 102, 158, 218, 317, 440, 613, 832, 1147, 1530, 2054, 2710, 3580, 4673, 6094, 7858, 10140, 12958, 16549, 20976, 26565, 33401, 41954, 52404, 65365, 81119, 100534, 124048, 152820, 187578, 229848, 280708, 342262, 416056, 504943, 611202, 738590, 890379 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 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, Comm. Algebra 22, No. 13, 5175-5193 (1994). FORMULA Expansion of (B*(A)^2 + 4*q^3/(B*(A)^2))/(B)^2, where A = q^(1/2)*((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4)*eta(q^11)*eta(q^44))) and B = q^(1/2)*(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22))), in powers of q. - G. C. Greubel, Jun 21 2018 a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(3/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018 EXAMPLE T22a = 1/q + 3*q + 4*q^3 + 11*q^5 + 17*q^7 + 31*q^9 + 45*q^11 + 71*q^13 + ... MATHEMATICA eta[q_]:= q^(1/24)*QPochhammer[q]; e44b := q^(1/2)*(eta[q]*eta[q^11]/(eta[q^2]*eta[q^22])); e88A := q^(1/2)*((eta[q^2]*eta[q^22])^2/(eta[q]*eta[q^4]*eta[q^11]*eta[q^44])); a:= CoefficientList[Series[ (e44b*(e88A)^2 + 4*q^3/(e44b*(e88A)^2))/(e44b)^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *) PROG (PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4)* eta(q^11) *eta(q^44))); B = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22))); Vec((B*(A)^2 + 4*q^3/(B*(A)^2))/(B)^2) \\ G. C. Greubel, Jun 21 2018 CROSSREFS Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc. Sequence in context: A026676 A142870 A143680 * A231882 A026753 A027222 Adjacent sequences:  A058566 A058567 A058568 * A058570 A058571 A058572 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2000 EXTENSIONS Terms a(12) onward added by G. C. Greubel, Jun 21 2018 STATUS approved

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)