A058576 McKay-Thompson series of class 24F for Monster.

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

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 * A360893 A365696 A346734

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