A007251 - OEIS

A007251

McKay-Thompson series of class 5A for the Monster group.
(Formerly M5396)

1, 0, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920

(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..10000

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 (eta(q) / eta(q^5))^6 + 6 + 125 * (eta(q^5) / eta(q))^6 in powers of q. - Michael Somos, Jul 05 2014

a(n) = A045482(n) = A244745(n) unless n=0.

a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Dec 04 2015

a(n) = A106248(n) + 125*A121591(n) for n > 0. - Seiichi Manyama, Mar 31 2017

EXAMPLE

T5A = 1/q + 134*q + 760*q^2 + 3345*q^3 + 12256*q^4 + 39350*q^5 + ...

MATHEMATICA

a[ n_] := With[ {A = (QPochhammer[ q] / QPochhammer[ q^5])^6 / q}, SeriesCoefficient[ A + 6 + 125 / A, {q, 0, n}]]; (* Michael Somos, Jul 05 2014 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x + A) / eta(x^5 + A))^6; polcoeff( A + 6*x + x^2 * 125 / A, n))}; /* Michael Somos, Jul 05 2014 */

CROSSREFS

Cf. A045482, A244745.

Sequence in context: A177348 A275997 A370162 * A219443 A348815 A230699

Adjacent sequences: A007248 A007249 A007250 * A007252 A007253 A007254

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved