A058559 McKay-Thompson series of class 20d for Monster.

1, 0, 3, -4, 4, -4, 7, -12, 13, -16, 22, -28, 38, -44, 55, -72, 83, -104, 129, -156, 187, -220, 273, -328, 384, -452, 539, -652, 757, -880, 1041, -1220, 1428, -1652, 1924, -2244, 2585, -2992, 3458, -3992, 4581, -5244, 6053, -6936, 7910, -9024, 10303, -11784, 13380, -15176, 17257, -19584

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..5000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of sqrt( 4 + (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^4 ) in powers of q. - G. C. Greubel, Jun 14 2018

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

Example

T20d = 1/q + 3*q^3 - 4*q^5 + 4*q^7 - 4*q^9 + 7*q^11 - 12*q^13 + 13*q^15 - ...

Mathematica

QP = QPochhammer; A = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40;
CoefficientList[Sqrt[A], q] (* Georg Fischer, Nov 15 2020 *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff(sqrtn( (eta(x + A) * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, 2), n))} /* Georg Fischer, Nov 15 2020 [adapted from Michael Somos' PARI in A058098] */

Crossrefs

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

Cf. A058098, A112158, A132040.

Sequence in context: A283972 A213509 A112180 * A232092 A345196 A185271

Adjacent sequences: A058556 A058557 A058558 * A058560 A058561 A058562

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 14 2018

Status

approved