A112163 Coefficients of replicable function number 24e.

1, 1, 3, -3, 6, 3, 10, -1, 15, 0, 24, -3, 37, 9, 57, -12, 84, 12, 118, -9, 165, 6, 228, -12, 316, 27, 432, -42, 582, 42, 776, -28, 1023, 24, 1344, -45, 1757, 82, 2283, -111, 2946, 111, 3774, -91, 4812, 84, 6108, -123, 7725, 208, 9732, -279, 12204, 282, 15240, -234, 18957

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..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

Example

G.f. = 1 + x + 3*x^2 - 3*x^3 + 6*x^4 + 3*x^5 + 10*x^6 - x^7 + 15*x^8 + 24*x^10 + ...
T24e = 1/q + q + 3*q^3 - 3*q^5 + 6*q^7 + 3*q^9 + 10*q^11 - q^13 + 15*q^15 + 24*q^19 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; e24F := q^(1/4)*(eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^3; a[n_]:= SeriesCoefficient[(e24F/.{q -> q^2}) + q/(e24F/.{q -> q^2}), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 14 2018 *)
a[ n_] := With[ {A = (QPochhammer[ x^4] QPochhammer[ x^6] / (QPochhammer[ x^2] QPochhammer[ x^12]))^3}, SeriesCoefficient[ A + x / A, {x, 0, n}]]; (* Michael Somos, Feb 18 2018 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); A = (eta(x^4 + A) * eta(x^6 + A) / (eta(x^2 + A) * eta(x^12 + A)))^3; polcoeff( A + x / A, n))}; /* Michael Somos, Feb 18 2018 */

Crossrefs

Sequence in context: A130695 A308083 A181788 * A058587 A196439 A184389

Adjacent sequences: A112160 A112161 A112162 * A112164 A112165 A112166

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved