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 A007251 McKay-Thompson series of class 5A for the Monster group. (Formerly M5396) 4
 1, 0, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = -1..10000 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339. D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278. FORMULA Expansion of (eta(q) / eta(q^5))^6 + 6 + 125 * (eta(q^5) / eta(q))^6 in powers of q. - Michael Somos, Jul 05 2014 a(n) = A045482(n) = A244745(n) unless n=0. a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Dec 04 2015 a(n) = A106248(n) + 125*A121591(n) for n > 0. - Seiichi Manyama, Mar 31 2017 EXAMPLE T5A = 1/q + 134*q + 760*q^2 + 3345*q^3 + 12256*q^4 + 39350*q^5 + ... MATHEMATICA a[ n_] := With[ {A = (QPochhammer[ q] / QPochhammer[ q^5])^6 / q}, SeriesCoefficient[ A + 6 + 125 / A, {q, 0, n}]]; (* Michael Somos, Jul 05 2014 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x + A) / eta(x^5 + A))^6; polcoeff( A + 6*x + x^2 * 125 / A, n))}; /* Michael Somos, Jul 05 2014 */ CROSSREFS Cf. A045482, A244745. Sequence in context: A051387 A177348 A275997 * A219443 A230699 A038369 Adjacent sequences:  A007248 A007249 A007250 * A007252 A007253 A007254 KEYWORD nonn AUTHOR STATUS approved

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