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A136570 McKay-Thompson series of class 29A for the Monster group with a(0) = 2. 2
1, 2, 3, 4, 7, 10, 17, 22, 32, 44, 62, 80, 112, 144, 193, 248, 323, 410, 530, 664, 845, 1054, 1324, 1634, 2037, 2498, 3082, 3760, 4601, 5580, 6789, 8186, 9891, 11876, 14271, 17052, 20393, 24260, 28876, 34224, 40557, 47888, 56540, 66516, 78240 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..1000

K. Bringmann and H. Swisher, On a conjecture of Koike on identities between Thompson series and Roger-Ramanujan functions, Proc. Amer. Math. Soc. 135 (2007), 2317-2326. See page 2325 (A.9).

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339. See page 335.

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

G.f.: x^(-1) * ( G(x) * G(x^29) + x^6 * H(x) * H(x^29) )^2 where G() is g.f. of A003114 and H() is g.f. of A003106.

a(n) ~ exp(4*Pi*sqrt(n/29)) / (sqrt(2)*29^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

EXAMPLE

q^-1 + 2 + 3*q + 4*q^2 + 7*q^3 + 10*q^4 + 17*q^5 + 22*q^6 + 32*q^7 + ...

MATHEMATICA

QP = QPochhammer; G[q_]:= QPochhammer[q^2, q^5]*QPochhammer[q^3, q^5] QPochhammer[q^5]/QPochhammer[q]; H[q_] := QPochhammer[q, q^5]* QPochhammer[q^4, q^5]*QPochhammer[q^5]/QPochhammer[q]; a[n_]:= SeriesCoefficient[(1/q)*(G[q]*G[q^29] + q^6*H[q]*H[q^29])^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Mar 21 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( sqr( 1 / prod(k=1, ceil(n / 5), (1 - x^(5*k-1)) * (1 - x^(5*k-4)), 1 + A) / prod(k=1, ceil(n / 145), (1 - x^(145*k-29)) * (1 - x^(145*k-116)), 1 + A) + x^6 / prod(k=1, ceil(n / 5), (1 - x^(5*k-2)) * (1 - x^(5*k-3)), 1 + A) / prod(k=1, ceil(n / 145), (1 - x^(145*k-58)) * (1 - x^(145*k-87)), 1 + A)), n))}

CROSSREFS

Cf. A058611(n) = a(n) unless n=0.

Sequence in context: A051449 A018143 A281839 * A082766 A119016 A082958

Adjacent sequences:  A136567 A136568 A136569 * A136571 A136572 A136573

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 07 2008

STATUS

approved

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Last modified January 16 03:30 EST 2019. Contains 319184 sequences. (Running on oeis4.)