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A058658 McKay-Thompson series of class 38a for Monster. 1
1, 2, 1, 3, 4, 7, 8, 13, 15, 21, 26, 35, 42, 56, 67, 86, 106, 132, 158, 199, 236, 290, 346, 420, 500, 603, 711, 850, 1002, 1189, 1393, 1648, 1922, 2258, 2629, 3075, 3566, 4153, 4801, 5569, 6421, 7420, 8528, 9831, 11268, 12942, 14801, 16949, 19337, 22090, 25140, 28644, 32536, 36978 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of (T19A + 4)^(1/2), where T19A = A058549, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(2*n/19)) / (2^(3/4) * 19^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T38a = 1/q + 2*q + q^3 + 3*q^5 + 4*q^7 + 7*q^9 + 8*q^11 + 13*q^13 + 15*q^15 + ...

MATHEMATICA

QP := QPochhammer; nmax = 100; G[q_] := 1/(QP[q, q^5]*QP[q^4, q^5]); H[q_] := 1/(QP[q^2, q^5]*QP[q^3, q^5]); T19A := -3 + (G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q; a:= CoefficientList[Series[(q*(T19A + 4) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

PROG

(PARI) q='q+O('q^40);  A = (eta(q)*eta(q^19)/(eta(q^2)*eta(q^38)))^2; B = - (eta(-q)*eta(-q^19)/(eta(q^2)*eta(q^38)))^2; T19A = (q^4/(A*B) - (A + B)/(4*q))^3; v=Vec((q^2 + T19A)^(1/2)); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jun 25 2018

CROSSREFS

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

Sequence in context: A075616 A160186 A050041 * A070827 A160191 A268613

Adjacent sequences:  A058655 A058656 A058657 * A058659 A058660 A058661

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 24 2018

STATUS

approved

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Last modified November 21 09:13 EST 2018. Contains 317431 sequences. (Running on oeis4.)