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 A132130 McKay-Thompson series of class 10D for the Monster group with a(0) = 6. 4
 1, 6, 21, 62, 162, 378, 819, 1680, 3276, 6138, 11145, 19662, 33840, 57048, 94362, 153432, 245757, 388218, 605466, 933414, 1423614, 2149586, 3215844, 4769544, 7016572, 10243896, 14848809, 21378276, 30582360, 43484304, 61473438, 86428896 (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). The g.f. is denoted by x_10 in Cooper 2012. LINKS Seiichi Manyama, Table of n, a(n) for n = -1..10000 S. Cooper, Sporadic sequences, modular forms and new series for 1/pi, Ramanujan J. (2012). Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-1) * (chi(-q^5) / chi(-q))^6 in powers of q where chi() is a Ramanujan theta function. Expansion of (eta(q^2) * eta(q^5) / (eta(q) * eta(q^10)))^6 in powers of q. Euler transform of period 10 sequence [ 6, 0, 6, 0, 0, 0, 6, 0, 6, 0, ...]. G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = (v - u^2) * (v - w^2) - u*w * (12*(1 + v^2) - 20*v). G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = f(t) where q = exp(2 Pi i t). G.f.: x^(-1) * (Product_{k>0} (1 + x^k) / (1 + x^(5*k)))^6. G.f.: 1 / ( x * Product_{k>0} P(10,x^k)^6 ) where P(n,x) is the n-th cyclotomic polynomial. a(n) = A058100(n) unless n=0. a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 06 2015 EXAMPLE G.f. = 1/q + 6 + 21*q + 62*q^2 + 162*q^3 + 378*q^4 + 819*q^5 + 1680*q^6 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ q^-1 (QPochhammer[ q^5, q^10] / QPochhammer[ q, q^2])^6, {q, 0, n}]; (* Michael Somos, Dec 07 2013 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^5 + A) / (eta(x + A) * eta(x^10 + A)))^6, n))}; CROSSREFS Cf. A058100. Sequence in context: A048476 A122678 A256569 * A022571 A321947 A291226 Adjacent sequences:  A132127 A132128 A132129 * A132131 A132132 A132133 KEYWORD nonn AUTHOR Michael Somos, Aug 11 2007, Aug 09 2008 EXTENSIONS Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)