OFFSET
-3,2
COMMENTS
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = -3..10000
Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.
Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]
FORMULA
Expansion of q^-3 * psi(q)^6 * phi(-q)^2 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos, Apr 24 2014
Expansion of eta(q^2)^10 * eta(q^3)^14 / (eta(q)^2 * eta(q^6)^22) in powers of q.
Euler transform of period 6 sequence [2, -8, -12, -8, 2, 0, ...]. - Michael Somos, Nov 10 2005
Convolution product of A128632, A128633, and A105559 (all three of them are modular functions and McKay-Thompson series of class 6E for the monster group). - Michael Somos, May 23 2014
EXAMPLE
G.f. = q^-3 + 2*q^-2 - 5*q^-1 - 24 - 23*q + 76*q^2 + 249*q^3 + 168*q^4 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^2]^10*(QP[q^3]^14/(QP[q]^2*QP[q^6]^22)) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-3, 0, n+=3; A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A)^14 / (eta(x + A)^2 * eta(x^6 + A)^22), n))}; /* Michael Somos, Nov 10 2005 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
STATUS
approved