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A007251 McKay-Thompson series of class 5A for the Monster group.
(Formerly M5396)
4
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: A051387 A177348 A275997 * A219443 A230699 A038369

Adjacent sequences:  A007248 A007249 A007250 * A007252 A007253 A007254

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 17 15:22 EDT 2018. Contains 313816 sequences. (Running on oeis4.)