0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

J. W. L. Glaisher, On the representation of a number as a sum of 14 and 16 squares, Quart. J. Math. 38 (1907), 178-236 (see p. 198).

F. Hirzebruch et al., Manifolds and Modular Forms, Vieweg 1994 p 133.

Ishikawa, T., Congruences between binomial coefficients binom(2f,f) and Fourier coefficients of certain eta-products, Hiroshima Math. J. 22 (1992), no. 3, 583-590.

M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.

H.-G. Quebbemann, Lattices with theta-functions for G(sqrt(2)) and linear codes, J. Algebra, 105 (1987), 443-450.

G. Shimura, Modular forms of half-integral weight, pp. 57-74 of Modular Functions of One Variable I (Antwerp 1972), Lect. Notes Math. 320 (1973).

T. D. Noe, Table of n, a(n) for n=0..1001

Expansion of cusp form (e(1)-e(2))(e(1)-e(3))(e(2)-e(3))^2 for GAMMA_0(2).

Euler transform of period 2 sequence [ -8,-16,...] (if offset -1). Expansion of (eta(q)eta(q^2))^8 in powers of q. - Michael Somos, Mar 18 2003

a(n) is multiplicative with a(2^e) = (-8)^e, a(p^e) = a(p)*a(p^(e-1)) - p^7*a(p^(e-2)) . - Michael Somos Mar 08 2006

Given A=A0+A1+A2+A3 is the 4-section, then 0=A2^3 +2*A0*(A1^2+A3^2) -4*A1*A2*A3 -3*A0^2*A2. - Michael Somos Mar 08 2006

t1 := product((1-q^m)^8, m=1..40): subs(q=q^2, t1): series(q*t1*%, q, 40);

(PARI) a(n)=local(A); if(n<1, 0, n--; A=x^n*O(x); polcoeff((eta(x+A)*eta(x^2+A))^8, n)) /* Michael Somos, Jul 16 2004 */

Sequence in context: A069186 A166625 A038290 this_sequence A137232 A147764 A162466

Adjacent sequences: A002285 A002286 A002287 this_sequence A002289 A002290 A002291

sign,easy,nice,mult

N. J. A. Sloane (njas(AT)research.att.com).

Extended, better description Jan 15 1996.