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A058512 Coefficients of replicable function number 15a. 1
1, 0, 5, -2, 0, 10, -1, 0, 25, 2, 0, 50, 1, 0, 100, 4, 0, 170, -6, 0, 305, -2, 0, 500, 2, 0, 825, 0, 0, 1300, 10, 0, 2040, -14, 0, 3100, -5, 0, 4700, 8, 0, 6950, 4, 0, 10225, 20, 0, 14800, -28, 0, 21285, -10, 0, 30200, 14, 0, 42625, 4, 0, 59500, 39, 0, 82610, -56, 0, 113690, -20, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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

Expansion of A + 5*q^2/A, where A = q*(eta(q^3)/eta(q^15))^2, in powers of q. - G. C. Greubel, Jun 21 2018

EXAMPLE

T15a = 1/q + 5*q - 2*q^2 + 10*q^4 - q^5 + 25*q^7 + 2*q^8 + 50*q^10 + q^11 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; e15D := q^(1/3)*(eta[q]/eta[q^5])^2;

a[n_]:= SeriesCoefficient[(e15D /. {q -> q^3}) + 5*q^2/(e15D /. {q -> q^3}), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 14 2018 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^3 + A) / eta(x^15 + A))^2; polcoeff( A + 5*x^2 / A, n))}; /* Michael Somos, Feb 18 2018 */

CROSSREFS

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

Sequence in context: A257406 A269980 A319231 * A111560 A324609 A211991

Adjacent sequences:  A058509 A058510 A058511 * A058513 A058514 A058515

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(24) onward added by G. C. Greubel, Feb 14 2018

STATUS

approved

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