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A058723 McKay-Thompson series of class 58a for the Monster group. 1
1, 1, 1, 1, 2, 2, 4, 3, 5, 6, 7, 8, 11, 12, 15, 17, 21, 23, 29, 32, 39, 44, 52, 58, 69, 77, 90, 101, 117, 132, 153, 170, 195, 219, 249, 278, 317, 352, 399, 444, 501, 557, 627, 694, 779, 864, 965, 1067, 1192, 1316, 1464, 1616, 1793, 1976, 2191, 2409, 2665, 2930 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

K. Bringmann and H. Swisher, On a conjecture of Koike on identities between Thompson series and Rogers-Ramanujan functions, Proc. Amer. Math. Soc. 135 (2007), no. 8, 2317-2326. (MR230255) see p. 2325 (A.9).

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

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

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

EXAMPLE

T58a = 1/q + q + q^3 + q^5 + 2*q^7 + 2*q^9 + 4*q^11 + 3*q^13 + 5*q^15 + ...

MATHEMATICA

QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A:= G[x^29]*G[x^1] + x^6*H[x^29]*H[x^1]; a:= CoefficientList[Series[A, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 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))} /* Michael Somos, Jan 07 2008 */

CROSSREFS

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

Sequence in context: A318632 A094051 A159268 * A329436 A182577 A241450

Adjacent sequences:  A058720 A058721 A058722 * A058724 A058725 A058726

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)