login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058576 McKay-Thompson series of class 24F for Monster. 3
1, 3, 6, 10, 15, 24, 37, 57, 84, 118, 165, 228, 316, 432, 582, 776, 1023, 1344, 1757, 2283, 2946, 3774, 4812, 6108, 7725, 9732, 12204, 15240, 18957, 23508, 29065, 35826, 44022, 53924, 65868, 80256, 97557, 118305, 143118, 172726, 208002, 249972, 299825, 358926, 428844, 511416, 608796 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

G.f. = 1 + 3*x + 6*x^2 + 10*x^3 + 15*x^4 + 24*x^5 + 37*x^6 + 57*x^7 + 84*x^8 + ...

T24F = 1/q + 3*q^3 + 6*q^7 + 10*q^11 + 15*q^15 + 24*q^19 + 37*q^23 + 57*x^27 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; e24F := q^(1/4)*(eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^3;  Table[SeriesCoefficient[e24F, {q, 0, n}], {n, 0, 50}] (* G. C. Greubel, Feb 14 2018 *)

a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2] QPochhammer[ x^3] / (QPochhammer[ x] QPochhammer[ x^6]))^3, {x, 0, n}]; (* Michael Somos, Feb 18 2018 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^3 + A) / (eta(x + A) * eta(x^6 + A)))^3, n))}; /* Michael Somos, Feb 18 2018 */

CROSSREFS

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

Sequence in context: A024674 A026104 A261632 * A230364 A214282 A130200

Adjacent sequences:  A058573 A058574 A058575 * A058577 A058578 A058579

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(6) onward added by G. C. Greubel, Feb 14 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 13:52 EST 2019. Contains 319271 sequences. (Running on oeis4.)