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A003295 McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
(Formerly M3872)
3
1, -5, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

Coefficients of a modular function denoted by B(tau) in Atkin (1967).

REFERENCES

A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76; see p. 42.

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

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=-1..30.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Contribution of Michael Somos, Aug 31 2012: (Start)

Expansion of -11 + (1 + 3*F)^2 * (1/F + 1 + 3*F) where F = eta(q^3) * eta(q^33) / (eta(q) * eta(q^11)) (= g.f. of A128663) in powers of q.

G.f. is Fourier series of a level 11 modular function. f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t).

A000521(n) = a(n) + 11 * a(11*n) unless n=0. [Atkin (1967) p. 22]

a(n) = A003295(n) = A058205(n) = A128525(n) = A134784(n) unless n=0. (End)

EXAMPLE

G.f. = 1/q - 5 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...

CROSSREFS

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

Cf. A003295, A058205, A128525, A128663, A134784.

Sequence in context: A146264 A146216 A046787 * A228857 A011853 A215053

Adjacent sequences:  A003292 A003293 A003294 * A003296 A003297 A003298

KEYWORD

sign,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 05 2000

STATUS

approved

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Last modified November 27 13:25 EST 2014. Contains 250196 sequences.