A058102 McKay-Thompson series of class 10a for Monster.

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

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