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A007252 McKay-Thompson series of class 5B for the Monster group with a(0) = 0.
(Formerly M4599)
3
1, 0, 9, 10, -30, 6, -25, 96, 60, -250, 45, -150, 544, 360, -1230, 184, -675, 2310, 1410, -4830, 750, -2450, 8196, 4920, -16180, 2376, -7875, 25644, 15000, -48720, 7126, -22800, 73221, 42310, -134760, 19284, -61400, 194334, 110610, -349000, 49563, -155250, 486370 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

REFERENCES

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

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..1000

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

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.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of 6 + (eta(q) / eta(q^5))^6 in powers of q. - Michael Somos, Apr 30 2004

a(n) = A045483(n) = A106248(n) unless n=0.

a(n) = A229793(n) - A078905(n) for n > 0. - Seiichi Manyama, Jan 01 2017

EXAMPLE

T5B = 1/q + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 - ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 6 + 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}]; (* Michael Somos, May 22 2013 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 6*x + (eta(x + A) / eta(x^5 + A))^6, n))}; /* Michael Somos, Apr 30 2004 */

(PARI) {a(n) = my(A, k); if( n<-1, 0, k = (sqrtint(40*n + 48) + 7)\10; A = x * (sum(i=-k, k, (-1)^i * x^((5*i^2 + 3*i)/2), x^2 * O(x^n)) / sum(i=-k, k, (-1)^i * x^((5*i^2 + i)/2), x^2 * O(x^n)))^5; polcoeff( 1/A - A - 5, n))}; /* Michael Somos, Apr 30 2004 */

CROSSREFS

Cf. A045483, A106248. (same except for initial terms).

Sequence in context: A041168 A042635 A045483 * A322653 A119209 A289520

Adjacent sequences:  A007249 A007250 A007251 * A007253 A007254 A007255

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 18 07:12 EST 2019. Contains 319269 sequences. (Running on oeis4.)