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A058571 McKay-Thompson series of class 24A for Monster. 2
1, 3, 3, 7, 18, 21, 30, 57, 75, 104, 156, 207, 293, 411, 525, 712, 984, 1248, 1622, 2169, 2757, 3530, 4560, 5736, 7284, 9249, 11472, 14374, 18078, 22242, 27484, 34140, 41787, 51184, 62796, 76317, 92893, 112998, 136275, 164671 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution cube of A112206. - Vaclav Kotesovec, Mar 12 2017

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 (terms 0..50 from G. A. Edgar)

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 q^(1/2) * (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) in powers of q. - G. A. Edgar, Mar 11 2017

a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 12 2017

EXAMPLE

T24A = 1/q + 3*q + 3*q^3 + 7*q^5 + 18*q^7 + 21*q^9 + 30*q^11 + 57*q^13 + ...

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 12 2017 *)

PROG

(PARI) q='q+O('q^66); Vec( (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) ) \\ Joerg Arndt, Mar 11 2017

CROSSREFS

Cf. A000521, A007240, A014708, A007241, A007267, A045478, A112206, etc.

Sequence in context: A032294 A146034 A032029 * A058492 A221303 A221378

Adjacent sequences:  A058568 A058569 A058570 * A058572 A058573 A058574

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Offset corrected by N. J. A. Sloane, Feb 17 2014

More terms from G. A. Edgar, Mar 11 2017

STATUS

approved

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Last modified December 17 02:31 EST 2018. Contains 318192 sequences. (Running on oeis4.)