OFFSET
0,2
COMMENTS
Although Watson says these are the coefficients theta_n defined on page 128, it appears that this is a mistake, and they are really the coefficients theta'_n. The true theta_n are given in A160528.
Watson's main reason for computing this sequence was to study values of n such that partition(49n+47) == 0 mod 343 (cf. A160553).
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
N. J. A. Sloane, Table of n, a(n) for n = 0..199
Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. See p. 128.
FORMULA
Expansion of q^(-23/24) * eta(q)^2 * eta(q^7)^3 in powers of q. - Michael Somos, May 31 2012
Euler transform of period 7 sequence [ -2, -2, -2, -2, -2, -2, -5, ...]. - Michael Somos, May 31 2012
G.f.: Product_{k>0} (1 - x^k)^2 * (1 - x^(7*k))^3. - Michael Somos, May 31 2012
EXAMPLE
G.f. = 1 - 2*x - x^2 + 2*x^3 + x^4 + 2*x^5 - 2*x^6 - 3*x^7 + 4*x^8 + x^9 - 5*x^10 + ...
G.f. = q^23 - 2*q^47 - q^71 + 2*q^95 + q^119 + 2*q^143 - 2*q^167 - 3*q^191 + 4*q^215 + ...
MAPLE
M1:=2400:
fm:=mul(1-x^n, n=1..M1):
B:=x*subs(x=x^24, fm):
C:=x^7*subs(x=x^168, fm):
t1:=B^2*C^3;
t2:=series(t1, x, M1);
t3:=subs(x=y^(1/24), t2/x^23);
t4:=series(t3, y, M1/24);
t5:=seriestolist(t4); # A002300
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^7]^3, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^7 + A)^3, n))}; /* Michael Somos, May 31 2012 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Nov 14 2009
STATUS
approved