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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
OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
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 A322465 A353600
KEYWORD
sign
STATUS
approved