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A058638 McKay-Thompson series of class 34A for Monster. 2
1, 0, 3, 2, 5, 6, 12, 12, 22, 22, 39, 40, 63, 68, 106, 112, 164, 182, 257, 282, 390, 432, 584, 652, 859, 964, 1253, 1404, 1794, 2024, 2556, 2880, 3594, 4054, 5016, 5662, 6930, 7830, 9516, 10744, 12959, 14640, 17546, 19800, 23590, 26612, 31536, 35560, 41919 (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).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -1/2 + ( 25/4 + T17A(q) + T17A(q^2) )^(1/2), where T17A(q) = A058530, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(2*n/17)) / (2^(3/4) * 17^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T34A = 1/q + 3*q + 2*q^2 + 5*q^3 + 6*q^4 + 12*q^5 + 12*q^6 + 22*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q];  nmax = 110;  A:= q^(1/2)*(eta[q^4]^2 *(eta[q^34]^5/(eta[q]*eta[q^2]*eta[q^17]^3*eta[q^68]^2)) - eta[q^2]^5*(eta[q^68]^2/(eta[q]^3*eta[q^4]^2*eta[q^17]*eta[q^34]))); T17A := (A^2 - 2*q)/q; T34A := -q/2 + q*((25/4) + T17A + (T17A /. {q -> q^2}) + O[q]^nmax)^(1/2);  a:= CoefficientList[Series[T34A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

CROSSREFS

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

Sequence in context: A286111 A240574 A050061 * A201218 A139140 A047074

Adjacent sequences:  A058635 A058636 A058637 * A058639 A058640 A058641

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 20 2014

STATUS

approved

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Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)