|
Search: id:A115110
|
|
|
| A115110 |
|
Expansion of q^(-1/24)eta(q)^3/eta(q^2) in powers of q. |
|
+0
1
|
|
| 1, -3, 1, 2, 2, -1, -4, 1, -2, 0, 2, 4, -1, 2, -2, -1, 0, -2, -2, -2, 0, 4, 1, 0, 2, -2, 5, 0, -2, 0, 0, -4, -2, 0, 0, -3, 4, 0, 0, -2, 1, 4, 2, 2, 0, 0, 0, -2, -2, 0, 2, -3, -2, 0, -2, 2, -4, 1, 0, 0, 0, 4, 2, 0, 4, 0, -4, 2, 0, 2, -1, 0, 0, 2, -2, -2, -6, -1, 2, 0, 0, -4, 0, 2, 2, 0, 0, 2, -2, 2, 2, 0, 1, 0, 0, 2, 4, 0, 0, -2, 1, -6, 0, -2, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
B. Gordon and D. Sinor, Multiplicative properties of eta-products, Number theory, Madras 1987, pp. 173-200, Lecture Notes in Math., 1395, Springer, Berlin, 1989. see page 182. MR1019331 (90k:11050)
George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113-134 see page 124 (5.15)
|
|
FORMULA
|
Expansion of phi(-q)f(-q) in powers of q where phi(),f() are Ramanujan theta functions.
Given A=A0+A1+A2+A3+A4+A5+A6 is the 7-section, then 0=A0*A4+A1*A3+A5*A6+4*A2^2, A2=x^2*A(x^49).
a(49n+2)=a(n). a(7n+2)=0 unless n=7k.
G.f.: Product_{k>0} (1-x^k)^2/(1+x^k).
G.f.: sum_{k>=0} ( x^((3k^2+k)/2)(1-x^(2k+1))*sum_{|j|<=k}(-x)^(-j^2) ).
Euler transform of period 2 sequence [ -3, -2,...].
Expansion of f(q)f(-q) in powers of q^2 where f() is a Ramanujan theta function.
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)^3/eta(x^2+A), n))}
|
|
CROSSREFS
|
A107033(n)=(-1)^n*a(n).
Sequence in context: A088429 A111951 A107033 this_sequence A066635 A016568 A021888
Adjacent sequences: A115107 A115108 A115109 this_sequence A115111 A115112 A115113
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Mar 07 2006
|
|
|
Search completed in 0.002 seconds
|
