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.
FORMULA
Expansion of 6 + (eta(q) / eta(q^5))^6 in powers of q. - Michael Somos, Apr 30 2004
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
KEYWORD
sign
AUTHOR
STATUS
approved