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A112165 McKay-Thompson series of class 24h for the Monster group. 5
1, 1, -1, 1, 2, -1, -2, -1, 3, 0, -4, 1, 5, 1, -7, 0, 8, 0, -10, -1, 13, -2, -16, 0, 20, 3, -24, 2, 30, -2, -36, -4, 43, 0, -52, 3, 61, 2, -73, 1, 86, -1, -102, -3, 120, -4, -140, 1, 165, 8, -192, 5, 224, -6, -260, -10, 301, -2, -348, 7, 401, 7, -462, 2, 530, -2, -608, -8, 696, -10, -796, 3, 909, 18, -1035, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Convolution square is A187197. - Michael Somos, Aug 31 2014

Expansion of chi(-x^4)^2 * chi(-x^12)^2 / (chi(-x^2)  * chi(-x^6)) in powers of x where chi() is a Ramanujan theta function. - Michael Somos, Apr 22 2015

a(n) = A255391(2*n - 1) = A255396(2*n - 1). - Michael Somos, Apr 22 2015

EXAMPLE

G.f. = 1 + x - x^2 + x^3 + 2*x^4 - x^5 - 2*x^6 - x^7 + 3*x^8 - 4*x^10 + ...

T24h = 1/q + q - q^3 + q^5 + 2*q^7 - q^9 - 2*q^11 - q^13 + 3*q^15 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2] QPochhammer[ x^6])^3 / (QPochhammer[ x] QPochhammer[ x^3] QPochhammer[ x^4]^2 QPochhammer[ x^12]^2), {x, 0, n}]; (* Michael Somos, Aug 31 2014 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^6 + A)^3 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A)^2 * eta(x^12 + A)^2), n))}; /* Michael Somos, Aug 31 2014 */

CROSSREFS

Cf. A187197, A255391, A255396.

Sequence in context: A245714 A092953 A058574 * A112186 A112187 A074093

Adjacent sequences:  A112162 A112163 A112164 * A112166 A112167 A112168

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)