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A058102 McKay-Thompson series of class 10a for Monster. 1
1, 8, 35, 100, 260, 548, 1191, 2340, 4525, 8320, 14838, 25828, 44070, 73500, 120695, 194408, 309459, 485400, 753025, 1154260, 1751419, 2631924, 3920625, 5790400, 8486720, 12343172, 17832027, 25588580, 36495125, 51738640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The convolution square of this sequence is A007251 except for the constant term: T10a(q)^2 = T5A(q^2) + 16. - G. A. Edgar, Apr 03 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..500 from G. A. Edgar)

D. Alexander, C. Cummins, J. McKay and C. Simons, Completely Replicable Functions, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.

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

a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

EXAMPLE

T10a = 1/q + 8*q + 35*q^3 + 100*q^5 + 260*q^7 + 548*q^9 + 1191*q^11 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 100; T5A := 6 +(eta[q]/eta[q^5] )^6 + 125*(eta[q^5]/eta[q])^6; a:= CoefficientList[Series[((q (T5A + 16) + O[q]^nmax // Normal /. {q -> q^2}) + O[q]^nmax)^(1/2) // Normal, {q, 0, nmax}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 05 2018 *)

PROG

(PARI)

t(q)=(eta(q)/eta(q^5))^6 / q + 6 + 125 * q * (eta(q^5)/eta(q))^6; \\ A007251

s(q)=sqrt(t(q^2) + 16);

v=Vec( s('q+O('q^100) ) );

vector(#v\2, n, v[2*n-1])

\\ Joerg Arndt, May 19 2018

CROSSREFS

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

Sequence in context: A265840 A212903 A168566 * A212674 A279743 A189592

Adjacent sequences:  A058099 A058100 A058101 * A058103 A058104 A058105

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)