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A058097 McKay-Thompson series of class 10A for Monster. 2
1, 0, 22, 56, 177, 352, 870, 1584, 3412, 5952, 11442, 19240, 34377, 56256, 95560, 151824, 247965, 385024, 609756, 927864, 1431094, 2139680, 3228516, 4752896, 7038610, 10215552, 14885450, 21330480, 30643161, 43407680, 61571148, 86305680, 121034807, 168032768 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..10000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Wikipedia, Higman-Sims group.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 30 2017

a(n) = A132040(n) + 16*A093831(n) = A132041(n) + 25*A227213(n) = A132130(n) + A284629(n) for n > 0. - Seiichi Manyama, Mar 31 2017

Expansion of A - 6 + 1/A, where A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10) ))^6, in powers of q. - G. C. Greubel, Jun 13 2018

EXAMPLE

T10A = 1/q + 22*q + 56*q^2 + 177*q^3 + 352*q^4 + 870*q^5 + 1584*q^6 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[(4*x*Product[((1 + x^k)*(1 + x^(5*k)))^2, {k, 1, nmax}] + Product[(1/(1 + x^(5*k))/(1 + x^k))^2, {k, 1, nmax}])^2 - 4*x, {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 30 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-6 + (eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^6 + (eta[q]*eta[q^10]/( eta[q^2]*eta[q^5]))^6), {q, 0, 60}, Assumptions->q>0], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 13 2018 *)

PROG

(PARI) q='q+O('q^30); A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^6/q; Vec(A - 6 + 1/A) \\ G. C. Greubel, Jun 13 2018

CROSSREFS

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A289015 A063302 A088820 * A131878 A019506 A202387

Adjacent sequences:  A058094 A058095 A058096 * A058098 A058099 A058100

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 19 2014

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)